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ormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterZeroOULaw","name":"Complex.imCLM.eq_1","type_dependencies":["Complex","Complex.addCommGroup","Complex.imCLM","Complex.imCLM._proof_2","Complex.imLm","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","Eq","LinearMap.mkContinuous","Module.complexToReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instOne","Real.instRing","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Eq.refl","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevRealSplit","name":"Complex.measurableEquivRealProd.eq_1","type_dependencies":["Complex","Complex.borelSpace","Complex.equivRealProdCLM","Complex.instAddCommMonoid","Complex.instNormedField","Complex.measurableEquivRealProd","Complex.measurableEquivRealProd._proof_1","Complex.measurableSpace","ContinuousLinearEquiv.toHomeomorph","Eq","Homeomorph.toMeasurableEquiv","MeasurableEquiv","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instMeasurableSpace","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instTopologicalSpaceProd"],"value_dependencies":["Complex","Complex.measurableEquivRealProd","Complex.measurableSpace","Eq.refl","MeasurableEquiv","Prod","Prod.instMeasurableSpace","Real","Real.measurableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteLaguerreOperator","name":"Complex.ofRealHom.eq_1","type_dependencies":["Complex","Complex.instSemiring","Complex.ofReal","Complex.ofRealHom","Complex.ofReal_add","Complex.ofReal_mul","Complex.ofReal_one","Complex.ofReal_zero","Eq","MonoidHom.mk","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NonAssocSemiring.toMulZeroOneClass","OneHom.mk","Real","Real.semiring","RingHom","RingHom.mk","Semiring.toNonAssocSemiring"],"value_dependencies":["Complex","Complex.instSemiring","Complex.ofRealHom","Eq.refl","Real","Real.semiring","RingHom","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterZeroOULaw","name":"Complex.reCLM.eq_1","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.reCLM","Complex.reCLM._proof_2","Complex.reLm","ContinuousLinearMap","Eq","LinearMap.mkContinuous","Module.complexToReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule"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ernativeBakryEmeryBrownianDyadicGaussianFinite","name":"GinibrePoincare.BakryBrownianFiniteDyadicIndex","type_dependencies":["Nat"],"value_dependencies":["Fin","Fin.val","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","Option","Sigma","instHPow","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianGlobalPath","name":"GinibrePoincare.BakryBrownianGlobalSample","type_dependencies":[],"value_dependencies":["GinibrePoincare.BakryBrownianDyadicCompletedSample","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryHilbertLift","name":"GinibrePoincare.BakryEmeryHilbertBlock","type_dependencies":["Nat"],"value_dependencies":["Complex","EuclideanSpace","Fin","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.BakryEmeryScalarFormAmbient","type_dependencies":["Real"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","GinibrePoincare.BakryEmeryScalarL2","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarMeasure","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.BakryEmeryScalarL2","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","GinibrePoincare.bakryEmeryScalarMeasure","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarMeasure","MeasureTheory.Lp","OfNat.ofNat","Real","Real.measurableSpace","Real.normedAddCommGroup","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.BakryEmeryScalarL2._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BernoulliCubeLSI","name":"GinibrePoincare.BernoulliCube","type_dependencies":["Nat"],"value_dependencies":["GinibrePoincare.BernoulliCube._f","Nat","Nat.brecOn"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BernoulliCubeLSI","name":"GinibrePoincare.BernoulliCube._f","type_dependencies":["Nat","Nat.below"],"value_dependencies":["Bool","GinibrePoincare.BernoulliCube.match_1","Nat","Nat.below","Nat.succ","OfNat.ofNat","PProd","Prod","Unit","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BernoulliCubeLSI","name":"GinibrePoincare.BernoulliCube._sunfold","type_dependencies":["Nat"],"value_dependencies":["Bool","GinibrePoincare.BernoulliCube","GinibrePoincare.BernoulliCube.match_1","Nat","Prod","Unit"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BernoulliCubeLSI","name":"GinibrePoincare.BernoulliCube._unsafe_rec","type_dependencies":["Nat"],"value_dependencies":["Bool","GinibrePoincare.BernoulliCube._unsafe_rec","GinibrePoincare.BernoulliCube.match_1","Nat","Prod","Unit"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BernoulliCubeExpectations","name":"GinibrePoincare.BernoulliCube.eq_1","type_dependencies":["Eq","GinibrePoincare.BernoulliCube","Nat","OfNat.o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o","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexHermite","name":"GinibrePoincare.ComplexHermite.Z.eq_1","type_dependencies":["Complex","Complex.instCommSemiring","Eq","Fin.instOfNat","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermite.Z._proof_1","GinibrePoincare.ComplexHermiteIndex","MvPolynomial.X","Nat","OfNat.ofNat","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.Z"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteHermiteDeficit","name":"GinibrePoincare.ComplexHermite.activeAntiDegrees","type_dependencies":["Complex","Complex.instZero","Finset","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","Nat"],"value_dependencies":["Complex","Complex.instZero","Finset.image","Finsupp","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","Nat","instDecidableEqNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteBinomialIdentity","name":"GinibrePoincare.ComplexHermite.alternating_vandermonde","type_dependencies":["Eq","Finset.range","Finset.sum","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instAddCommMonoid","Int.instMonoid","Int.instMul","Int.instNegInt","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.decLe","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite"],"value_dependencies":["AddCommGroupWithOne.toAddGroupWithOne","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instAddMonoidHomClass","AddMonoidHom.instFunLike","AddMonoidHom.mk","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Finset","Finset.instSetLike","Finset.mem_range","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_congr","Finsupp","Finsupp.instFunLike","HAdd.hAdd","HMul","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Int","Int.cast","Int.cast_neg","Int.cast_one","Int.instAddCommMonoid","Int.instAddMonoid","Int.instCommRing","Int.instCommSemiring","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instRing","Int.instSemiring","LE.le","LT.lt","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_atom","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.choose","Nat.decLe","Nat.instCommSemiring","Nat.instMonoid","Nat.le_of_lt_succ","Nat.rawCast","Nat.succ","Neg.neg","NegZeroClass.toNeg","NonAssocCommRing.toNonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.C","Polynomial.C_mul","Polynomial.C_pow","Polynomial.X","Polynomial.coeff","Polynomial.coeff_C_mul","Polynomial.coeff_X_add_one_pow","Polynomial.coeff_X_pow_mul'","Polynomial.coeff_add","Polynomial.coeff_zero","Polynomial.commRing","Polynomial.commSemiring","Polynomial.instAdd","Polynomial.instMul","Polynomial.instNatCast","Polynomial.instOne","Polynomial.ring","Polynomial.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","Semirin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Monoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.succ","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRingHomClass.toMulHomClass","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instIsOrderedRing","Real.instMul","Real.instNatCast","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_mul","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toNonUnitalRingHomClass","Semiring.toModule","Semiring.toNonAssocSemiring","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.HermiteWirtinger.0.GinibrePoincare.ComplexHermite.dbarOne_diagonalEval","congr","congrArg","congrFun'","eq_self","id","instHMul","instHSub","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instSubNat","map_mul","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteWirtinger","name":"GinibrePoincare.ComplexHermite.dbarOne_normalizedEval_public","type_dependencies":["Complex","Complex.instMul","Complex.ofReal","Eq","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.normalizedEval","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Real.sqrt","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dependencies":["Complex","Complex.instMul","Complex.ofReal","Eq","Eq.mpr","GinibrePoincare.ComplexHermite.dbarOne","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.dbarOnePublic_eq_dbarOne","GinibrePoincare.ComplexHermite.dbarOne_normalizedEval","GinibrePoincare.ComplexHermite.normalizedEval","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Real.sqrt","congrArg","id","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteRodriguesGaussian","name":"GinibrePoincare.ComplexHermite.dbarOne_rodriguesGaussian","type_dependencies":["Complex","Complex.instMul","Complex.instNatCast","Complex.instNeg","Eq","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.rodriguesGaussian","HMul.hMul","Nat","Nat.cast","Neg.neg","instHMul"],"value_dependencies":["AddCancelMonoid.toAddRightCancelMonoid","AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddRightCancelMonoid.toAddRightCancelSemigroup","AddRightCancelSemigroup.toIsRightCancelAdd","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.im","Complex.instAdd","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedField","Complex.instOne","Complex.instZero","Complex.ofReal","Complex.re","Complex.re_add_im","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.ComplexHermite.dbarOne._proof_1","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.fderiv_rodriguesGaussian","GinibrePoincare.ComplexHermite.rodriguesGaussian","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.LinearCombination.mul_const_eq","Mathlib.Tactic.Ring.Commo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ormedField.toNontriviallyNormedField","Eq","Exists","Field.toSemifield","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.diagonalEval","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidHomClass.toAddHomClass","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.conjCLE","Complex.differentiable_conj","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instT2Space","Complex.instZero","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.hasFDerivAt","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.zero","DFunLike.coe","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.ext","Fin.instOfNat","Fin.val","Fin.val_eq_zero_iff._simp_1","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.diagonalEval","GinibrePoincare.ComplexHermiteIndex","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Matrix.cons_val_fin_one","Matrix.vecCons","Matrix.vecEmpty","Monoid.toNPow","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","MvPolynomial.induction_on","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","Nat.succ","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologic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ibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family_mem_antiDegreeClosedSpan","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.ComplexHermite.zeroAntiCoefficients","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HSMul.hSMul","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.smul_mem","Submodule.sum_mem","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_self","fact_one_le_two_ennreal","id","instDecidableEqNat","instHSMul","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","not_false_eq_true","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteHermiteDeficit","name":"GinibrePoincare.ComplexHermite.finiteHermiteDeficit","type_dependencies":["Complex","Complex.instZero","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","LT.lt","Nat","OfNat.ofNat","Real","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteDbarEnergy","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.finiteHermiteDeficit._proof_1","GinibrePoincare.ComplexHermite.finiteHermiteDeficit._proof_2","GinibrePoincare.ComplexHermite.positiveAntiCoefficients","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteHermiteDeficit","name":"GinibrePoincare.ComplexHermite.finiteHermiteDeficit._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteHermiteDeficit","name":"GinibrePoincare.ComplexHermite.finiteHermiteDeficit._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"ki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uousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection._proof_1","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_1","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_2","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_4","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_5","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.ComplexHermite.hermiteL2Family_mem_antiDegreeClosedSpan","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","Iff.mpr","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.starProjection","Submodule.starProjection_eq_self_iff","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.HermiteL2Family","name":"GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.in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.normSq","DFunLike.coe","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.complexGaussianMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat"],"value_dependencies":["CommRing.toCommMonoid","Complex","Complex.commRing","Complex.im","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.re","DFunLike.coe","Eq","Eq.mpr","Eq.trans","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.integrable_normSq_normalizedEval","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianProbability","HAdd.hAdd","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.fintype_prod","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.ProbabilityMeasure.instIsProbabilityMeasureToMeasure","MeasureTheory.ProbabilityMeasure.pi","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.sigmaFinite_of_locallyFinite","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toMonoidHomClass","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instCommMonoid","Real.instMul","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","funext","id","instHAdd","instHMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat","map_prod","of_eq_true","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MultivariateHermiteIntegrability","name":"GinibrePoincare.ComplexHermite.integrable_normSq_normalizedEval","type_dependencies":["Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.complexCoordinateGaussianProbability","LT.lt","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.instCommSemiring","Complex.instMul","Complex.instNorm","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","Complex.normSq","Complex.sq_norm","Continuous.aestronglyMeasurable","Continuous.comp","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.ofNNReal","ENorm.enorm","Eq","Eq.mpr","Eq.symm","Eq.trans","Filter.univ_mem'","Function.comp","GinibrePoincare.ComplexHermite.continuous_normalizedEval","GinibrePoincare.ComplexHermite.integrable_conj_normalizedEval_mul","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.complexCoordinateGaussianProbability","HMul.hMul","HPow.hPow","LT.lt","MeasureTheory.Integrable.congr'_enorm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace",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oMetricSpace","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","congrArg","id","instCountableFin","instHPow","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","propext","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.mem_support_loweredCoefficients_iff","type_dependencies":["And","Complex","Complex.instZero","Eq","Exists","Fin","Finset","Finset.instSetLike","Finsupp","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.lowerHermiteIndex","GinibrePoincare.ComplexHermite.loweredCoefficients","Iff","LT.lt","Membership.mem","Nat","OfNat.ofNat","Prod.snd","SetLike.instMembership","instLTNat","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Complex","Complex.addGroupWithOne","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instZero","Complex.ofReal","Complex.ofReal_inj._simp_1","DFunLike.coe","Decidable.byContradiction","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Fin","Fin.fintype","Finset","Finset.decidableExistsAndFinsetCoe","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Fintype.decidablePiFintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.lowerHermiteIndex","GinibrePoincare.ComplexHermite.loweredCoefficients","GinibrePoincare.ComplexHermite.loweredCoefficients_apply_eq_zero_of_offImage","GinibrePoincare.ComplexHermite.loweredCoefficients_apply_lowerHermiteIndex","HMul.hMul","Iff.intro","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","LT.lt.ne'","Mathlib.Tactic.Push.not_and_eq","Mathlib.Tactic.Push.not_exists._simp_1","Membership.mem","Nat","Nat.cast","Nat.cast_mul._simp_1","Nat.cast_pos'","Nat.cast_zero","Nat.decLt","Ne","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod.snd","Real","Real.instAddCommMonoid","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","Zero.toOfNat0","binderNameHint","cast","congrArg","congrFun'","forall_congr","id","implies_congr","instDecidableAnd","instDecidableEqNat","instDecidableEqProd","instHMul","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","mul_ne_zero","mul_pos","propext"]},{"kind":"definition","module":"GinibrePoincare.Analysis.HermiteMonomialSpan","name":"GinibrePoincare.ComplexHermite.mixedMonomialRectangleSpan","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Nat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","Submodule"],"value_dependencies":["And","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instSemiring","Complex.instStarRing","DFunLike.coe","Eq","Exists","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Pi.Function.module","Pi.addCommMonoid","RingHom","RingHom.instFunLike","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.ofPred","Submodule.span","instHMul","instHPow","instLENat","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteMonomialSpan","name":"GinibrePoincare.ComplexHermite.mixedMonomialRectangleSpan_mono","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","GinibrePoincare.ComplexHermite.mixedMonomialRectangleSpan","LE.le","Nat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Preorder.toLE","Semiring.toModule","Submodule","Submodule.instPartialOrder","instLENat"],"value_dependencies":["And","And.casesOn","And.intro","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Compl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upp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.W","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermite.Z._proof_1","GinibrePoincare.ComplexHermite.normalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.ComplexHermite.raw","GinibrePoincare.ComplexHermiteIndex","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","LT.lt","Matrix.cons_val_fin_one","Matrix.vecCons","Matrix.vecEmpty","Membership.mem","Min.min","Monoid.toNPow","MonoidWithZeroHomClass.toMonoidHomClass","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.C_mul","MvPolynomial.C_neg","MvPolynomial.C_pow","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.factorial","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.succ","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRingHomClass.toMulHomClass","OfNat.ofNat","Real","Real.instInv","Real.instMul","Real.instNatCast","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","congr","congrArg","congrFun'","eq_self","funext","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLTNat","instMinNat","instOfNatNat","instSubNat","map_mul","map_natCast","map_neg","map_pow","map_sum","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteOrthogonalityCombinatorics","name":"GinibrePoincare.ComplexHermite.normalizedEval_inner_eq_momentSum_of_mixedMoments","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instStarRing","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","Eq","GinibrePoincare.ComplexHermite.MixedMomentFormula","GinibrePoincare.ComplexHermite.hermiteInnerMomentSum","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.complexCoordinateGaussianProbability","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Real","Real.instMul","Real.instRCLike","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","Algebra.toModule","CommGroupWithZero.toDivisionCommMonoid","CommMagma.toMul","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.conj_ofReal","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_mul","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","ENormedAddCommMonoid.toESeminormedAddCommMonoid","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Finset","Finset.instSetLike","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_comm","Finset.sum_congr","Finset.sum_mul","GinibrePoincare.ComplexHermite.MixedMomentFormula","GinibrePoincare.ComplexHermite.diagonalRawCoeff","GinibrePoincare.ComplexHermite.hermiteInnerMomentSum","GinibrePoincare.ComplexHermite.integrable_complex_monomial_complexCoordinateGaussianProbability","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.normalizedEval_eq_sum","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.complexCoordinateGaussianProbability","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HMul","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_prod_atom","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Integrable.const_mul","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integrable_finsetSum","MeasureTheory.integral","MeasureTheory.integral_const_mul","MeasureTheory.integral_finsetSum","Membership.mem","Min.min","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNRat","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.factorial","Nat.instCommSemiring","Nat.instMonoid","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalRingHomClass.toMulHomClass","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","RCLike.toStarRing","Real","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomCompTriple.comp_apply","RingHomInvPair.instStarRingEnd","RingHomInvPair.triples\u2082","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarMul.toInvolutiveStar","StarRing.toStarAddMonoid","StarRing.toStarMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","id","inferInstance","instAddNat","instCommSemiringNNRat","instDecidableEqNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instH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omplexHermite.totalAntiDegree","LT.lt","Nat","Nat.decLt","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["Complex","Complex.instZero","Eq.refl","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.positiveAntiCoefficients","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.raiseAt","type_dependencies":["Fin","Nat"],"value_dependencies":["Fin","Function.update","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.raiseAt.eq_1","type_dependencies":["Eq","Fin","Function.update","GinibrePoincare.ComplexHermite.raiseAt","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.ComplexHermite.raiseAt","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.raiseAt_lowerAt","type_dependencies":["Eq","Fin","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.raiseAt","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["Decidable.byContradiction","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Fin","Function.update","Function.update.congr_simp","Function.update_of_ne","Function.update_self","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.raiseAt","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","True","_private.GinibrePoincare.Analysis.HermiteEnergy.0.GinibrePoincare.ComplexHermite.raiseAt_lowerAt._proof_1_3","congrArg","congrFun'","dite","eq_self","funext","id","instAddNat","instDecidableEqFin","instDecidableEqNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.raiseHermiteIndex","type_dependencies":["Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","Nat"],"value_dependencies":["Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseAt","Nat","Prod.fst","Prod.mk","Prod.snd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.ComplexHermite.raiseHermiteIndex.eq_1","type_dependencies":["Eq","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.ComplexHermite.raiseHermiteIndex","Nat","Prod.fst","Prod.mk","Prod.snd"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteEnergy","name":"GinibrePoincare.ComplexHermite.raiseHermiteIndex_lowerHermiteIndex","type_dependencies":["Eq","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.lowerHermiteIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","LT.lt","Nat","OfNat.ofNat","Prod.snd","instLTNat","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.lowerHermiteIndex","GinibrePoincare.ComplexHermite.raiseAt_lowerAt","GinibrePoincare.ComplexHermite.raiseHermiteIndex","LT.lt","Nat","OfNat.ofNat","Prod.ext","Prod.fst","Prod.snd","instLTNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.ComplexHermite","name":"GinibrePoincare.ComplexHermite.raw","type_dependencies":["GinibrePoincare.ComplexHermite.Poly","Nat","Real"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instSemiring","Complex.ofReal","DFunLike.coe","Finset.range","Finset.sum","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.W","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermiteIndex","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Min.min","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.factorial","Nat.instAddMonoid","Nat.instMulZeroClass","Neg.neg","OfNat.ofNat","Real","RingHom","RingHom.instFunLike","Semiring.toMonoid","Semiring.toNonAssocSemiring","instAddNat","instHAdd","instHMul","instHPow","instHSub","instMinNat","instOfNatNat","instSubNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexHermite","name":"GinibrePoincare.ComplexHermite.raw.eq_1","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra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ocSemiring.toMulZeroClass","Not","OfNat.ofNat","One.toOfNat1","Order.lt_add_one_iff._simp_1","PartialOrder.toPreorder","Pi.instSub","Preorder.toLE","Preorder.toLT","Real","RingHom","RingHom.id","RingHom.instFunLike","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteLeading.0.GinibrePoincare.ComplexHermite.raw_leading_coefficient._proof_1_1","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteLeading.0.GinibrePoincare.ComplexHermite.raw_leading_coefficient._proof_1_2","addRightReflectLE_of_addLeftReflectLE","add_zero","and_self","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","eq_self","id","if_neg","imp_self._simp_1","implies_congr","instAddNat","instDecidableAnd","instDecidableEqFin","instDecidableEqNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instLENat","instLTNat","instMinNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instSubNat","ite","ite_eq_left_of_eq_true","le_inf_iff._simp_1","lt_add_iff_pos_left._simp_1","mul_one","not_false_eq_true","not_true_eq_false","of_eq_true","one_ne_zero._simp_1","pow_zero","tsub_self","tsub_zero","zero_le._simp_1","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexHermite","name":"GinibrePoincare.ComplexHermite.raw_one_one","type_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instRing","Complex.ofReal","DFunLike.coe","Eq","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.W","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermite.raw","GinibrePoincare.ComplexHermiteIndex","HMul.hMul","HSub.hSub","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","Real","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","instHMul","instHSub","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.addCommGroup","AddMonoidAlgebra.commRing","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instRing","Complex.instSemiring","Complex.ofReal","DFunLike.coe","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin.instOfNat","Finset","Finset.instSingleton","Finset.range","Finset.sum","Finset.sum_range_succ","Finset.sum_singleton","Finsupp","Finsupp.instAdd","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.W","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermite.Z._proof_1","GinibrePoincare.ComplexHermite.raw","GinibrePoincare.ComplexHermiteIndex","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_natSub","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_c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riviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instInv","Real.instNatCast","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.coe_eq_zero._simp_1","WithTop.one","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","id","inferInstance","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatNat","instOneENat","instSubNat","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","one_ne_zero._simp_1","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteRodriguesHolomorphicLowering","name":"GinibrePoincare.ComplexHermite.rodrigues_dhol_add","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAdd","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","GinibrePoincare.ComplexHermite.dholOne","HAdd.hAdd","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHAdd","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.ComplexHermite.dholOne","GinibrePoincare.ComplexHermite.dholOne._proof_1","GinibrePoincare.ComplexHermite.dholOne.eq_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsTopologicalAddGroup.toContinuousAdd","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring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incare.Analysis.GaussianLSIFiniteProduct","name":"GinibrePoincare.GaussianProductSpace._unsafe_rec","type_dependencies":["Nat"],"value_dependencies":["GinibrePoincare.GaussianProductSpace._unsafe_rec","GinibrePoincare.GaussianProductSpace.match_1","Nat","Prod","Real","Unit"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"GinibrePoincare.GaussianProductSpace.match_1","type_dependencies":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dependencies":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianBlockRadialLaw","name":"GinibrePoincare.GaussianRadialBlocks","type_dependencies":["Nat"],"value_dependencies":["Fin","Fin.val","GinibrePoincare.Configuration","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.GinibreComplexGradientPair","type_dependencies":["Nat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreComplexGradientPair._proof_1","GinibrePoincare.GinibreComplexGradientPair._proof_2","GinibrePoincare.GinibreComplexGradientSpace","GinibrePoincare.ginibreComplexEuclideanGradient._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.GinibreComplexGradientPair._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.GinibreComplexGradientPair._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.GinibreComplexGradientSpace","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.GinibreComplexGradientSpace","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.GinibreComplexGradientSpace","type_dependencies":["Nat"],"value_dependencies":["Complex","EuclideanSpace","Fin","Nat","OfNat.ofNat","Prod","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianMaximalNoiseTopology","name":"GinibrePoincare.GinibreContinuousNoise","type_dependencies":["Nat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Su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rePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreDifferentialDeficitVector","GinibrePoincare.ginibreDifferentialFirstDerivative","GinibrePoincare.ginibreDifferentialSecondDerivative","GinibrePoincare.ginibreDifferentialSecondEnergy","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Endgame.FullTheoremOneTen","name":"GinibrePoincare.GinibreDifferentialDeficits.recOn","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreDifferentialDeficits","GinibrePoincare.GinibreDifferentialDeficits.mk","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreDifferentialDeficitVector","GinibrePoincare.ginibreDifferentialFirstDerivative","GinibrePoincare.ginibreDifferentialSecondDerivative","GinibrePoincare.ginibreDifferentialSecondEnergy","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm",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AddGroup","AddSubgroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.Lp","Nat","OfNat.ofNat","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.GinibreFullComplexL2._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.GinibreFullFormAmbient","type_dependencies":["Nat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.GinibreFullFormAmbient._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.GinibreFullFormAmbient._proof_2","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.GinibreFullFormAmbient._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.GinibreFullGradientL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","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MulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.L2_boundedCoefficient_memLp","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.MemLp.toLp","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.norm","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.L2_boundedCoefficient_memLp","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","IsOrderedRing.toMulPosMono","LE.le","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.norm","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat","mul_le_mul_of_nonneg_right","norm_nonneg","norm_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.L2BoundedCoefficientConvergence","name":"GinibrePoincare.L2_boundedCoefficient_tendsto","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","GinibrePoincare.L2_boundedCoefficient_memLp","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.norm","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","Su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ormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.eval","Polynomial.eval_smul","Polynomial.instZero","Polynomial.module","Polynomial.semiring","Polynomial.smulZeroClass","ProbabilityTheory.gammaMeasure","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","True","congrArg","congrFun'","eq_self","funext","instDistribOfSemiring","instHMul","instHSMul","instMulZeroClassOfSemiring","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LaguerreGammaOrthogonality","name":"GinibrePoincare.Laguerre.gammaIntegral.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.Laguerre.gammaIntegral","LT.lt","LinearMap","Nat","OfNat.ofNat","Polynomial","Polynomial.module","Polynomial.semiring","Real","Real.instAddCommMonoid","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","instLTNat","instOfNatNat"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.Laguerre.gammaIntegral","LT.lt","LinearMap","Nat","OfNat.ofNat","Polynomial","Polynomial.module","Polynomial.semiring","Real","Real.instAddCommMonoid","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GammaPolynomialMoments","name":"GinibrePoincare.Laguerre.gammaIntegral.eq_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddHom.mk","Eq","GinibrePoincare.Laguerre.gammaIntegral","GinibrePoincare.Laguerre.gammaIntegral._proof_1","GinibrePoincare.Laguerre.gammaIntegral._proof_2","InnerProductSpace.toNormedSpace","LT.lt","LinearMap","LinearMap.mk","MeasureTheory.integral","Nat","Nat.cast","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.eval","Polynomial.module","Polynomial.semiring","ProbabilityTheory.gammaMeasure","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","instLTNat","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.Laguerre.gammaIntegral","LT.lt","LinearMap","Nat","OfNat.ofNat","Polynomial","Polynomial.module","Polynomial.semiring","Real","Real.instAddCommMonoid","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GammaPolynomialMoments","name":"GinibrePoincare.Laguerre.gammaIntegral_monomial","type_dependencies":["DFunLike.coe","Eq","GinibrePoincare.Laguerre.gammaIntegral","GinibrePoincare.Laguerre.gammaMoment","HMul.hMul","LT.lt","LinearMap","LinearMap.instFunLike","Nat","OfNat.ofNat","Polynomial","Polynomial.module","Polynomial.monomial","Polynomial.semiring","Real","Real.instAddCommMonoid","Real.instMul","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["CommSemiring.toSemiring","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","Eq","Eq.trans","Field.toSemifield","GinibrePoincare.Laguerre.gammaIntegral","GinibrePoincare.Laguerre.gammaMoment","GinibrePoincare.Laguerre.integral_pow_gamma","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","LinearMap","LinearMap.instFunLike","MeasureTheory.integral","MeasureTheory.integral_const_mul","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.eval","Polynomial.eval_monomial","Polynomial.module","Polynomial.monomial","Polynomial.semiring","ProbabilityTheory.gammaMeasure","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","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ifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GammaPolynomialMoments.0.GinibrePoincare.Laguerre.gammaMoment_succ._proof_1_1","_private.GinibrePoincare.Analysis.GammaPolynomialMoments.0.GinibrePoincare.Laguerre.gammaMoment_succ._proof_1_2","congrArg","congrFun'","id","instAddNat","instDecidableEqNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instSubNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralizedLaguerre","name":"GinibrePoincare.Laguerre.hasDerivAt_derivative","type_dependencies":["CommSemiring.toSemiring","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","GinibrePoincare.Laguerre.polynomial","HasDerivAt","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","Polynomial","Polynomial.derivative","Polynomial.eval","Polynomial.module","Polynomial.semiring","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instPolynormableSpace"],"value_dependencies":["DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","GinibrePoincare.Laguerre.polynomial","LinearMap","LinearMap.instFunLike","Nat","Polynomial","Polynomial.derivative","Polynomial.hasDerivAt","Polynomial.module","Polynomial.semiring","Real","Real.denselyNormedField","Real.semiring","RingHom.id","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralizedLaguerre","name":"GinibrePoincare.Laguerre.hasDerivAt_polynomial","type_dependencies":["CommSemiring.toSemiring","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","GinibrePoincare.Laguerre.polynomial","HasDerivAt","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","Polynomial","Polynomial.derivative","Polynomial.eval","Polynomial.module","Polynomial.semiring","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instPolynormableSpace"],"value_dependencies":["DenselyNormedField.toNontriviallyNormedField","GinibrePoincare.Laguerre.polynomial","Nat","Polynomial.hasDerivAt","Real","Real.denselyNormedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GammaPolynomialMoments","name":"GinibrePoincare.Laguerre.integrable_polynomial_gamma","type_dependencies":["LT.lt","MeasureTheory.Integrable","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.eval","ProbabilityTheory.gammaMeasure","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.instOne","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["CommRing.toNonUnitalCommRing","DFunLike.coe","Distrib.toAdd","Distrib.toMul","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mpr","GinibrePoincare.Laguerre.integrable_pow_gamma","HAdd.hAdd","HMul.hMul","HPow.hPow","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.const_mul","MeasureTheory.Integrable.fun_add","MeasureTheory.Measure","Monoid.toNPow","NPow.toPow","Nat","N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","Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.actualContractionLaplaceLinear","LE.le","LT.lt","LinearMap","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOperator","name":"GinibrePoincare.actualContractionLaplaceLinear_norm_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","GinibrePoincare.actualContractionLaplaceLinear","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And.right","BorelSpace.opensMeasurable","CompleteSpace","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Function.comp","GinibrePoincare.actualNormalizedLaplaceIntegral_norm_bound","HMul.hMul","HSMul.hSMul","LE.le","LT.lt","MeasureTheory.IntegrableOn","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integral","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NNReal","NNReal.instTopologicalSpace","Neg.neg","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.exp","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","Semiring.toNonAssocSemiring","Set.Ioi","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_real_toNNReal","instHMul","instHSMul","instSecondCountableTopologyReal","secondCountableTopologyEither_of_left"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOperator","name":"GinibrePoincare.actualContractionLaplaceOperator","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","LE.le","LT.lt","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","GinibrePoincare.actualContractionLaplaceLinear","GinibrePoincare.actualContractionLaplaceOperator._proof_2","LE.le","LT.lt","LinearMap.mkContinuous","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instOne","Real.instRing","Real.instZero","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOperator","name":"GinibrePoincare.actualContractionLaplaceOperator._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","GinibrePoincare.actualContractionLaplaceLinear","HMul.hMul","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instRing","Real.instZero","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Eq.mpr","GinibrePoincare.actualContractionLaplaceLinear","GinibrePoincare.actualContractionLaplaceLinear_norm_bound","HMul.hMul","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instTopologicalSpace","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instRing","Real.instZero","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHMul","instMulZeroOneClassOfSemiring","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOrbit","name":"GinibrePoincare.actualContractionLaplace_commutes","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HAdd.hAdd","HMul.hMul","HSMul.hSMul","LE.le","LT.lt","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Module.toDistribMulAction","NNReal","NNReal.instSemiring","NNReal.instTopologicalSpace","Neg.neg","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","Real.toNNReal","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set.Ioi","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.integral_comp_comm","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.actualContractionLaplace_integrable","HAdd.hAdd","HMul.hMul","HSMul","HSMul.hSMul","LE.le","LT.lt","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Module.toDistribMulAction","NNReal","NNReal.instSemiring","NNReal.instTopologicalSpace",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uence_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","StrictMono","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","And.casesOn","ContinuousENorm.toENorm","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Exists.casesOn","Filter.Eventually","Filter.EventuallyEq","Filter.EventuallyEq.rfl","Filter.Tendsto","Filter.Tendsto.comp","Filter.atTop","Filter.atTop_neBot","Filter.mp_mem","Filter.univ_mem'","Function.comp","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.TendstoInMeasure","MeasureTheory.TendstoInMeasure.congr","MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae","MeasureTheory.ae","MeasureTheory.tendstoInMeasure_of_tendsto_Lp","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","StrictMono","StrictMono.tendsto_atTop","Subtype","Subtype.val","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","fact_one_le_two_ennreal","id","instArchimedeanNat","instInhabitedNat","instIsDirectedOrder","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","nhds","tendsto_nhds_unique"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticEnergyCompactness","name":"GinibrePoincare.actualL2Limit_memLp_of_energy_bound","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","HPow.hPow","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddComm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der","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instClosedIciTopology","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsOrderedModule","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","le_of_not_gt","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceBounds","name":"GinibrePoincare.actualNormalizedLaplaceIntegral_norm_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Filter.Eventually","HMul.hMul","HSMul.hSMul","LE.le","LT.lt","MeasureTheory.AEStronglyMeasurable","MeasureTheory.IntegrableOn","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","Module.toDistribMulAction","Neg.neg","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","Set.Ioi","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.actualNormalizedLaplaceWeight_integrable","GinibrePoincare.actualNormalizedLaplaceWeight_mass","HMul.hMul","HSMul.hSMul","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","LE.le","LE.le.trans_eq","LT.lt","LT.lt.le","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.smul","MeasureTheory.Integrable","MeasureTheory.Integrable.aestronglyMeasurable","MeasureTheory.Integrable.const_mul","MeasureTheory.Integrable.mono'","MeasureTheory.Integrable.norm","MeasureTheory.IntegrableOn","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_const_mul","MeasureTheory.integral_mono_ae","MeasureTheory.norm_integral_le_integral_norm","Membership.mem","Module.toDistribMulAction","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Neg.neg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.measurableSpace","Real.measureSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Set","Set.Ioi","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","id","instClosedIciTopology","instDistribOfSemiring","instHMul","instHSMul","instHasSolidNormReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instPolynormableSpace","instTransEq_1","instTransLE","mul_comm","mul_le_mul_of_nonneg_left","mul_nonneg","mul_one","norm_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceBounds","name":"GinibrePoincare.actualNormalizedLaplaceWeight_integrable","type_dependencies":["HMul.hMul","LT.lt","MeasureTheory.IntegrableOn","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instLT","Real.instMul","Real.instNeg","Real.instPreorder","Real.instZero","Real.measureSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Integrable.const_mul","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NormedCommRing.toNormedRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.exp","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Re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italNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.mk","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.exp","Real.exp_zero","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.Ioi","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","eq_self","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsCancelMulZero","instMulZeroClassOfSemiring","instOfNat","integral_exp_mul_Ioi","lt_of_not_ge","ne_of_gt","neg_div_neg_eq","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovTiltLawLimit","name":"GinibrePoincare.actualRealDensity_integral","type_dependencies":["ENNReal.ofReal","Eq","Filter.EventuallyLE","HMul.hMul","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.ae","MeasureTheory.integral","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instZero","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.measurableSpace","ENNReal.measurable_ofReal","ENNReal.ofReal","ENNReal.ofReal_lt_top","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mpr","Eq.trans","Filter.Eventually.of_forall","Filter.EventuallyLE","Filter.mp_mem","Filter.univ_mem'","Function.comp","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable.comp_aemeasurable","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable.aemeasurable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","id","instHMul","instHSMul","integral_withDensity_eq_integral_toReal_smul\u2080","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianShiftedLimit","name":"GinibrePoincare.actualTendstoInMeasure_sub","type_dependencies":["EMetricSpace.toPseudoEMetricSpace"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actualDensity_continuous_test_tendsto","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Measurable.comp_aemeasurable","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_bdd","MeasureTheory.Integrable.sub","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.eLpNorm","MeasureTheory.integral","MeasureTheory.integral_add","MetricSpace","MetricSpace.toEMetricSpace","MetricSpace.toPseudoMetricSpace","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace","OfNat.ofNat","One.toOfNat1","Pi.instSub","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddMonoid","Real.instCommSemiring","Real.instLE","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring","Ring.toAddCommGroup","Ring.toSemiring","SecondCountableTopology","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","congr","congrArg","congrFun'","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instSecondCountableTopologyReal","nhds","norm_nonneg","rfl","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralInitialIntervalBound","name":"GinibrePoincare.actual_sum_range_le_support_bound","type_dependencies":["Eq","Finset.range","Finset.sum","HMul.hMul","LE.le","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instZero","Zero.toOfNat0","instHMul","instLENat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toNSMul","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","Eq.mpr","Eq.symm","Eq.trans","Finset","Finset.card","Finset.card_range","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.range_mono","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.sum_subset","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","HMul.hMul","HSMul.hSMul","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","LE.le","LT.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ountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","congrArg","id","instMeasurableSingletonClassOfMeasurableEq","instMetricSpaceNNReal","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instPseudoMetricSpaceNNReal","instT6SpaceOfMetrizableSpace","le_rfl","measurable_from_prod_countable_left","measurable_id","standardBorel_of_polish"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LipschitzMollification","name":"GinibrePoincare.ae_fderiv_mollification_tendsto","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiffBump.normed","ContinuousLinearMap","ContinuousLinearMap.lsmul","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.atTop","FiniteDimensional","GinibrePoincare.lsiMollifier","InnerProductSpace.toNormedSpace","IsScalarTower.right","LipschitzWith","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.convolution","MetricSpace.toEMetricSpace","NNReal","Nat","Nat.instPreorder","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivisionRing","Real.instRCLike","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instIsTopologicalAddGroupReal","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Algebra.to_smulCommClass","Bool","Bool.false","BorelSpace","BorelSpace.opensMeasurable","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable","ContDiffBump.normed","ContDiffBump.rIn","ContDiffBump.rOut","Continuous.locallyIntegrable","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.instBorelSpace","ContinuousLinearMap.instCompleteSpace","ContinuousLinearMap.instMeasurableSpace","ContinuousLinearMap.isScalarTower","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toNormedSpace._proof_1","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Eventually","Filter.Eventually.of_forall","Filter.Tendsto","Filter.atTop","FiniteDimensional","FiniteDimensional.proper_real","FirstCountableTopology.frechetUrysohnSpace","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","FrechetUrysohnSpace.to_sequentialSpace","GinibrePoincare.fderiv_normed_convolution_lipschitz","GinibrePoincare.ls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rePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.vandermondeSymmetricAlternatingEquiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv.symm","LinearIsometryEquiv.toContinuousLinearEquiv","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.subtypeL","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.alternatedInverseVandermondeL2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.alternatedInverseVandermondeL2_mem_gradedClosedSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClas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upp.instAddZeroClass","Fintype.card","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.alternatedMonomialPolynomial","GinibrePoincare.permutationSign","HMul.hMul","HPow.hPow","Inv.inv","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","NPow.toPow","Nat","Nat.cast","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","RingHom","RingHom.instFunLike","Semiring.toMonoid","Semiring.toNonAssocSemiring","instDecidableEqFin","instHMul","instHPow"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.alternatedMonomialPolynomial","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatedMonomialPolynomial","name":"GinibrePoincare.alternatedMonomialPolynomial_alternating","type_dependencies":["Complex","Fin","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.alternatedMonomialPolynomial","Nat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commRing","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","CharZero.infinite","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommMonoid","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instOne","Complex.instSemiring","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv.Perm","Equiv.Perm.instMul","Equiv.Perm.permGroup","Equiv.instEquivLike","Equiv.instFintype","Equiv.mulLeft","Equiv.sum_comp","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.prod","Finset.prod_congr","Finset.sum","Finset.sum_congr","Finset.univ","Finsupp","Finsupp.instAdd","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Fintype.card","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.alternatedMonomialPolynomial","GinibrePoincare.eval_permuteConfigurationPolynomial","GinibrePoincare.permutationSign","GinibrePoincare.permutationSign_mul_general","GinibrePoincare.permutationSign_sq_general","GinibrePoincare.permute","GinibrePoincare.permuteConfigurationPolynomial","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.RingNF.mul_assoc_rev","Mathlib.Tactic.RingNF.nat_rawCast_1","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","MvPolynomial.funext","NPow.toPow","Nat","Nat.cast","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRingHomClass.toMulHomClass","OfNat.ofNat","One.toOfNat1","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomC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erm.sign_swap'","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_left","Equiv.swap_apply_of_ne_of_ne","Equiv.swap_apply_right","EquivLike.toFunLike","Exists","Exists.casesOn","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.ParticlePermutation","GinibrePoincare.collisionSet","GinibrePoincare.permutationSign","GinibrePoincare.permute","Group.toDivInvMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasDistribNeg.toInvolutiveNeg","Iff.mp","Int","Int.cast","Int.cast_neg","Int.cast_one","Int.instCommRing","Int.instMonoid","Int.negOfNat","Int.ofNat","Int.rawCast","InvolutiveNeg.toNeg","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidHom","MonoidHom.instFunLike","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","One.toOfNat1","Or","Or.resolve_left","Ring","Ring.toAddCommGroup","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Units","Units.instMulOneClass","Units.instNeg","Units.instOne","Units.val","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_false","eq_self","funext","id","inferInstance","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_right_of_eq_false","mul_eq_zero","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.alternating_polynomial_division_of_dvd","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonUnitalSemiring","And","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Dvd.dvd","Eq","Exists","Fin","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.polynomialVandermonde","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonUnitalSemiring.toSemigroupWithZero","SemigroupWithZero.toSemigroup","instHMul","semigroupDvd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonUnitalSemiring","And","And.intro","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Dvd.dvd","Eq","Eq.ndrec","Eq.symm","Exists","Exists.casesOn","Exists.intro","Fin","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.isSymmetric_quotient_of_vandermonde_mul_al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ePoincare.bakryBoundedSpatialCutoff._proof_1","type_dependencies":["FiniteDimensional","HasContDiffBump","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"],"value_dependencies":["ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff.congr_simp","type_dependencies":["Eq","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"],"value_dependencies":["Eq","Eq.rec","Eq.refl","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","ContDiffBump.toFun","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialBump","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.bakryBoundedSpatialCutoff._proof_1","HAdd.hAdd","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHSMul"],"value_dependencies":["Eq.refl","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff_compact","type_dependencies":["BorelSpace","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Bool","BorelSpace","ContDiffBump.hasCompactSupport","ContDiffBump.toFun","DistribMulAction.toMulAction","DivisionSemiring.toGroupWithZero","Eq.refl","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialBump","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HasCompactSupport.comp_homeomorph","Homeomorph.smulOfNeZero","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSpace","Module.toDistribMulAction","Monoid.toSemigroup","MonoidWithZero.toMonoid","MulAction.toSemigroupAction","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddComm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.tendsto_atTop_add_const_right","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.bakryBoundedSpatialCutoff_derivative_bound","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Lattice.toSemilatticeInf","MeasurableSpace","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","Nat","Nat.cast","Nat.instPreorder","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instArchimedean","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","congrArg","congrFun'","div_eq_mul_inv","fderiv","funext","id","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOrderTopologyReal","nhds","norm_nonneg","squeeze_zero","tendsto_inv_atTop_zero","tendsto_natCast_atTop_atTop","tendsto_zero_iff_norm_tendsto_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CommSemiring.toSemiring","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialBump","GinibrePoincare.bakryBoundedSpatialCutoff","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","MeasurableSpace","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHAdd","instHMul","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","BorelSpace","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.differentiable","ContDiffBump.contDiff","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp_id","ContinuousLinearMap.comp_smul\u209b\u2097","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","ENat","Eq","Eq.mp","Eq.refl","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","Function.comp","GinibrePoincare.bakryBoundedSpatialBump","GinibrePoincare.bakryBoundedSpatialCutoff","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.const_smul","HasFDerivAt.fderiv","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsBoundedSMul.toUniformContinuousConstSMul","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instField","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","hasFDerivAt_id","id","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHMul","instHSMul","instIsTopologicalRingReal","instOneENat","instPolynormableSpace","instSMulOfMul","instZeroENat","map_inv\u2080","smulCommClass_self","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff_mem_unit","type_dependencies":["And","BorelSpace","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instLE","Real.instOne","Real.instRCLike","Real.instZero","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And.intro","BorelSpace","ContDiffBump.le_one","ContDiffBump.nonneg","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialBump","GinibrePoincare.bakryBoundedSpatialCutoff","HAdd.hAdd","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","LE.le","MeasurableSpace","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instDivisionRing","Real.instInv","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff_smooth","type_dependencies":["BorelSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CommMonoid.toMonoid","ContDiff.comp","ContDiffBump.contDiff","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENat","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialBump","HAdd.hAdd","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsBoundedSMul.toUniformContinuousConstSMul","MeasurableSpace","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instCommMonoid","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","contDiff_const_smul","instHAdd","instHSMul","instTopENat","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBoundedLSIClosure","name":"GinibrePoincare.bakryBoundedSpatialCutoff_tendsto","type_dependencies":["BorelSpace","Filter.Tendsto","Filter.atTop","FiniteDimensional","GinibrePoincare.bakryBoundedSpatialCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","Nat","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.continuous","ContDiffBump.one_of_mem_closedBall","ContDiffBump.toFun","ContDiffBump.toFun.congr_simp","Continuous.continuousAt","ContinuousAt.tendsto","Dist.dist","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Poincare.bakryBrownianDyadicCompletedMeasure","GinibrePoincare.bakryBrownianDyadicCompletedPath","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPath","MeasurableSpace.pi","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","Membership.mem","Min.min","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.covariance","PseudoMetricSpace.toUniformSpace","Real","Real.instMin","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["AEMeasurable","AEMeasurable.aestronglyMeasurable","AEMeasurable.comp_aemeasurable","BorelSpace.opensMeasurable","Continuous.measurable","ContinuousEvalConst.continuous_eval_const","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousEvalConst","ContinuousMap.instFunLike","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.symm","Function.comp","GinibrePoincare.BakryBrownianDyadicCompletedSample","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicCompletedMeasure","GinibrePoincare.bakryBrownianDyadicCompletedPath","GinibrePoincare.bakryBrownianDyadicCompleted_forget_measurePreserving","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPath","GinibrePoincare.bakryBrownianDyadicPath_aemeasurable","GinibrePoincare.bakryBrownianDyadicUniform_pathMeasurable","GinibrePoincare.bakryGlobalCovariance_pathBorel","Measurable.aemeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.map_eq","MeasureTheory.MeasurePreserving.measurable","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","Membership.mem","MetricSpace.toEMetricSpace","Min.min","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.covariance","ProbabilityTheory.covariance_map","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instMin","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instSecondCountableTopologyReal","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianGlobalGaussian","name":"GinibrePoincare.bakryBrownianDyadicCompletedPath_isGaussian_of_original","type_dependencies":["ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","GinibrePoincare.BakryBrownianDyadicCompletedSample","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicCompletedMeasure","GinibrePoincare.bakryBrownianDyadicCompletedPath","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPath","MeasurableSpace.pi","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","Membership.mem","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.IsGaussianProcess","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Semiring.toModule","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.opensMeasurable","Continuous.measurable","ContinuousEvalConst.continuous_eval_const","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousEvalConst","ContinuousMap.instFunLike","DFunLike.coe","Eq","Eq.mpr","Finset","Finset.instSetLike","Finset.restrict","GinibrePoincare.BakryBrownianDyadicCompletedSample","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianCompleted_pathMeasurable","GinibrePoincare.bakryBrownianDyadicCompletedMeasure","GinibrePoincare.bakryBrownianDyadicCompletedPath","GinibrePoincare.bakryBrownianDyadicCompletedPath_measurable","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPath","GinibrePoincare.bakryBrownianDyadic_completed_map","GinibrePoincare.instBorelSpaceContinuousMapElemRealIccOfNat_ginibrePoincare_1","Measurable.aemeasurable","Measurable.comp","Measurable.of_eval","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","Membership.mem","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","ProbabilityTheory.HasGaussianLaw.aemeasurable","ProbabilityTheory.HasGaussianLaw.isGaussian_map","ProbabilityTheory.HasGaussianLaw.mk","ProbabilityTheory.IsGaussian","Probabil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AddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instMin","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","neg_eq_zero","nhds","rfl","sub_eq_zero_of_eq","sub_zero","tendsto_const_nhds"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicLevel","type_dependencies":["ContinuousMap","Fin","HPow.hPow","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["ContinuousMap","ContinuousMap.instAddCommMonoidOfContinuousAdd","ContinuousMap.instSMul","DivInvMonoid.toDiv","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.bakryBrownianDyadicLevel._proof_1","GinibrePoincare.bakryBrownianDyadicLevel._proof_2","GinibrePoincare.bakryBrownianDyadicTent","GinibrePoincare.bakryBrownianDyadicTent._proof_2","HDiv.hDiv","HPow.hPow","HSMul.hSMul","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Real.sqrt","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHDiv","instHPow","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicLevel._proof_1","type_dependencies":["ContinuousConstSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instMul","Real.pseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicLevel._proof_2","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicLevel.eq_1","type_dependencies":["ContinuousMap","ContinuousMap.instAddCommMonoidOfContinuousAdd","ContinuousMap.instSMul","DivInvMonoid.toDiv","Eq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.bakryBrownianDyadicLevel","GinibrePoincare.bakryBrownianDyadicLevel._proof_1","GinibrePoincare.bakryBrownianDyadicLevel._proof_2","GinibrePoincare.bakryBrownianDyadicTent","GinibrePoincare.bakryBrownianDyadicTent._proof_2","HDiv.hDiv","HPow.hPow","HSMul.hSMul","Memb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ath","type_dependencies":["ContinuousMap","GinibrePoincare.BakryBrownianDyadicSample","Membership.mem","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instAdd","ContinuousMap.instAddCommMonoidOfContinuousAdd","ContinuousMap.instSMul","Fin","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicLevel","GinibrePoincare.bakryBrownianDyadicLinearPath","GinibrePoincare.bakryBrownianDyadicPartialPath._proof_1","GinibrePoincare.bakryBrownianDyadicPartialPath._proof_2","HAdd.hAdd","HPow.hPow","HSMul.hSMul","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","Option.none","Option.some","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Sigma","Sigma.mk","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHPow","instHSMul","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","tsum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadicPath.eq_1","type_dependencies":["ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instAdd","ContinuousMap.instAddCommMonoidOfContinuousAdd","ContinuousMap.instSMul","Eq","Fin","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicLevel","GinibrePoincare.bakryBrownianDyadicLinearPath","GinibrePoincare.bakryBrownianDyadicPartialPath._proof_1","GinibrePoincare.bakryBrownianDyadicPartialPath._proof_2","GinibrePoincare.bakryBrownianDyadicPath","HAdd.hAdd","HPow.hPow","HSMul.hSMul","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","Option.none","Option.some","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Sigma","Sigma.mk","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHPow","instHSMul","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","tsum"],"value_dependencies":["ContinuousMap","Eq.refl","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicPath","Membership.mem","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadicPath_aemeasurable","type_dependencies":["AEMeasurable","ContinuousMap","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPath","GinibrePoincare.bakryBrownianDyadicUniform_pathMeasurable","MeasurableSpace.pi","Membership.mem","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instMetricSpace","EMetricSpace.toPseudoEMetricSpace","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianDyadicPartialPath","GinibrePoincare.bakryBrownianDyadicPartialPath_measurable","GinibrePoincare.bakryBrownianDyadicPartialPath_tendsto","GinibrePoincare.bakryBrownianDyadicPath","GinibrePoincare.bakryBrownianDyadicUniform_pathBorel","GinibrePoincare.bakryBrownianDyadicUniform_pathMeasurable","Measurable.aemeasurable","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","Nat","OfNat.ofNat","One.toOfNat1","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_of_tendsto_metrizable_ae'","compactSpace_Icc","instOrderTopology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akryBrownianDyadicPath_endpoints._proof_3","GinibrePoincare.bakryBrownianDyadicTent","GinibrePoincare.bakryBrownianDyadicTent._proof_1","GinibrePoincare.bakryBrownianDyadicTent._proof_2","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","LinearOrder.toMin","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Max.max","Membership.mem","MetricSpace.toEMetricSpace","Min.min","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_le._simp_1","Nat.cast_nonneg","Nat.cast_one","Nat.cast_pow._simp_1","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Not","OfNat.ofNat","One.toOfNat1","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMax","Real.instMin","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.metricSpace","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommGroupWithZero","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toMulActionSemiHomClass","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set","Set.Elem","Set.Icc","Set.instMembership","SetLike.instMembership","Sigma","Sigma.mk","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","Subtype.val","Summable","SummationFilter","SummationFilter.instNeBotUnconditional","SummationFilter.unconditional","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","cast","congr","congrArg","congrFun'","dite","eq_self","funext","id","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalRingReal","instLENat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","inv_pow","map_smul","map_sum","max_eq_left","min_le_left","min_le_right","mul_one","neg_nonpos","of_eq_true","one_div","optParam","sub_nonpos","tsum","tsum_eq_zero_of_not_summable","tsum_zero","zero_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadicPath_endpoints._proof_1","type_dependencies":["LE.le","OfNat.ofNat","Preorder.toLE","Real","Real.instPreorder","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Bool","Bool.true","Eq.refl","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Nat.cast_zero","OfNat.ofNat","Real","Real.instIsOrderedRing","Real.instRing","Real.instZero","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadicPath_endpoints._proof_2","type_dependencies":["LE.le","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instOne","Real.instPreorder","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Bool","Bool.true","Eq.refl","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Nat.cast_one","Nat.cast_zero","OfNat.ofNat","One.toOfNat1","Real","Real.instIsOrderedRing","Real.instOne","Real.instRing","Real.instZero","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadicPath_endpoints._proof_3","type_dependencies":["LE.le","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instOne","Real.instPreorder"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Bool","Bool.true",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are.Analysis.AlternativeBakryEmeryBrownianDyadicCovariance","name":"GinibrePoincare.bakryBrownianDyadicResidual_tendsto","type_dependencies":["Filter.Tendsto","Filter.atTop","GinibrePoincare.bakryBrownianDyadicResidual","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set.Elem","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","nhds"],"value_dependencies":["AddGroup.existsAddOfLE","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And.left","And.right","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.div_const","Filter.atTop","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.bakryBrownianDyadicResidual","GinibrePoincare.bakryBrownianDyadicResidual_bounds","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","Int.ofNat","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_lt_true","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_le_true","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddGroup","Real.instArchimedean","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Set.Elem","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHDiv","instHMul","instHPow","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","inv_pow","nhds","one_div","squeeze_zero","tendsto_pow_atTop_nhds_zero_of_lt_one","zero_div"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicTent","type_dependencies":["ContinuousMap","Fin","HPow.hPow","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["ContinuousMap.mk","Fin","Fin.val","GinibrePoincare.bakryBrownianDyadicTent._proof_1","GinibrePoincare.bakryBrownianDyadicTent._proof_2","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Max.max","Membership.mem","Min.min","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instMonoid","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instMax","Real.instMin","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicTents","name":"GinibrePoincare.bakryBrownianDyadicTent._proo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rePoincare.bakryBrownianDyadicBadLevel","GinibrePoincare.bakryBrownianDyadicBadLevel._proof_1","GinibrePoincare.bakryBrownianDyadicBadLevel._proof_2","GinibrePoincare.bakryBrownianDyadicBadLevel_bound","GinibrePoincare.bakryBrownianDyadicFourthMoment","GinibrePoincare.bakryBrownianDyadicMeasure","GroupWithZero.toDivisionMonoid","HDiv.hDiv","HMul.hMul","HPow.hPow","Int.ofNat","Inv.inv","InvOneClass.toInv","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","IsTopologicalRing.toIsTopologicalSemiring","LE.le","LT.lt","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_lt_true","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_le_true","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.ae_eventually_notMem","Membership.mem","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Not","OfNat.ofNat","One.toOfNat1","Option.some","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.decidableLT","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toMonoidWithZero","Set","Set.instMembership","Set.ofPred","Sigma","Sigma.mk","Summable","Summable.mul_left","SummationFilter.unconditional","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","congrArg","div_pos","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","le_of_not_gt","mul_nonneg","ne_top_of_le_ne_top","pow_pos","summable_geometric_of_lt_one","tsum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianDyadicUniform","name":"GinibrePoincare.bakryBrownianDyadic_series_summable","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instAddCommMonoidOfContinuousAdd","Filter.Eventually","Fin","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.bakryBrownianDyadicLevel","GinibrePoincare.bakryBrownianDyadicMeasure","HPow.hPow","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","Option.some","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instOne","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Sigma","Sigma.mk","Summable","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instIsTopologicalRingReal","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompactlyCoherentSpace.of_sequentialSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","Co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oidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.bakryBrownianUnitClamp","GinibrePoincare.bakryBrownianUnitClamp._proof_1","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Max.max","Membership.mem","Min.min","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.decidableLE","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMax","Real.instMin","Real.instOne","Real.instPreorder","Real.instRing","Real.instSemilatticeInf","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.Icc.instOne","Set.Icc.instZero","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.mk","Subtype.mk.congr_simp","Subtype.val","True","Zero.toOfNat0","congr","congrArg","dite","eq_self","id","inf_of_le_right","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","le_of_not_gt","lt_of_not_ge","max_eq_left","max_eq_right","min_eq_left","min_eq_right","neg_neg_of_pos","of_eq_true","rfl","sub_self","sub_sub_cancel","sub_zero","zero_le_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianGlobalPath","name":"GinibrePoincare.bakryBrownianUnitClamp_zero_of_nonpos","type_dependencies":["And.intro","Eq","GinibrePoincare.bakryBrownianUnitClamp","GinibrePoincare.bakryBrownianUnitClamp_zero_of_nonpos._proof_1","GinibrePoincare.bakryBrownianUnitClamp_zero_of_nonpos._proof_2","LE.le","Membership.mem","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instLE","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","Zero.toOfNat0"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","And.intro","Eq","Eq.trans","GinibrePoincare.bakryBrownianUnitClamp","GinibrePoincare.bakryBrownianUnitClamp._proof_1","GinibrePoincare.bakryBrownianUnitClamp_zero_of_nonpos._proof_1","GinibrePoincare.bakryBrownianUnitClamp_zero_of_nonpos._proof_2","LE.le","Max.max","Membership.mem","Min.min","MulZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instIsOrderedRing","Real.instLE","Real.instMax","Real.instMin","Real.instOne","Real.instPreorder","Real.instSemilatticeInf","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.Icc.instZero","Set.instMembership","Subtype","Subtype.ext","Subtype.mk","Subtype.mk.congr_simp","Subtype.val","True","Zero.toOfNat0","congrArg","congrFun'","eq_self",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nalysis.AlternativeBakryEmeryLiftTransfer","name":"GinibrePoincare.bakryEmeryBlockLift_gradient","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.ginibreEuclideanGradient","HAdd.hAdd","HSMul.hSMul","Nat","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithLp.instSMul","deriv","instAddNat","instHAdd","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.differentiableAt","DifferentiableAt.hasDerivAt","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.trans","EuclideanSpace","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_coordinate","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasDerivAt.comp_hasFDerivAt","HasFDerivAt","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroOneClass.toMulOneClass","Nat","Nat.cast","Nat.cast_one","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.ext","PiLp.innerProductSpace._proof_1","PolynormableSpace.continuousSMul","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithLp.instSMul","WithLp.ofLp","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","deriv","fderiv","funext","id","instAddNat","instContinuousSMulForall","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLiftTransfer","name":"GinibrePoincare.bakryEmeryBlockLift_gradient_norm_sq","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.ginibreEuclideanGradient","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","Norm.norm","NormedField.toField","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.instNorm","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMonoid","Real.instMul","Real.instNatCast","Real.norm","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","deriv","instAddNat","instFintypeProd","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommMonoid.toMonoid","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryBlockLift_gradient","GinibrePoincare.configurationNormSq","GinibrePoincare.configurationNormSq_gradient_norm_sq","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.ginibreEuclideanGradient","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toNormSMulClass","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.instNormSMulClass","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","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trivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSMulOfMul","instSecondCountableTopologyReal","instZeroENat","secondCountableTopologyEither_of_right","smulCommClass_self","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianEndpoint","name":"GinibrePoincare.bakryEmeryBrownianEndpoint_measurable","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff","ConvexOn","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Fintype","Function.hasSMul","GinibrePoincare.bakryEmeryBrownianEndpoint","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","ProbabilityTheory.IsBrownianReal","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.univ","WithLp.instAddCommGroup","WithLp.instSMul","WithLp.measurableSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.mk","BorelSpace.opensMeasurable","CommSemiring.toSemiring","ContDiff","Continuous","Continuous.comp","Continuous.const_smul","Continuous.measurable","Continuous.prodMk","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousConstSMul","ContinuousMap.instSMul","ConvexOn","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Field.toSemifield","Finite.of_fintype","Finite.to_countable","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Fintype","Function.comp","Function.hasSMul","GinibrePoincare.bakryEmeryBrownianEndpoint","GinibrePoincare.bakryEmeryBrownianNoisePath","GinibrePoincare.bakryEmeryBrownianNoisePath_measurable","GinibrePoincare.bakryEmeryLangevinEndpoint","GinibrePoincare.bakryEmeryLangevinEndpoint_continuous","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","LE.le","LT.lt","Measurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instNorm","PiLp.instPseudoMetricSpace","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","PiLp.uniformSpace","ProbabilityTheory.IsBrownianReal","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","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brePoincare.Analysis.AlternativeBakryEmeryBrownianNoise","name":"GinibrePoincare.bakryEmeryBrownianNoisePath","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Membership.mem","NNReal","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ContinuousMap.instZero","ContinuousMap.mkD","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","GinibrePoincare.bakryEmeryBrownianNoiseReal","Membership.mem","NNReal","NegZeroClass.toZero","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","Zero.toOfNat0","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianNoise","name":"GinibrePoincare.bakryEmeryBrownianNoisePath.eq_1","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ContinuousMap.instZero","ContinuousMap.mkD","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","GinibrePoincare.bakryEmeryBrownianNoisePath","GinibrePoincare.bakryEmeryBrownianNoiseReal","Membership.mem","NNReal","NegZeroClass.toZero","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","Zero.toOfNat0","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","EuclideanSpace","GinibrePoincare.bakryEmeryBrownianNoisePath","Membership.mem","NNReal","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryBrownianNoise","name":"GinibrePoincare.bakryEmeryBrownianNoisePath_actual","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Filter.Eventually","Fintype","GinibrePoincare.bakryEmeryBrownianNoisePath","GinibrePoincare.bakryEmeryBrownianNoiseReal","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","ProbabilityTheory.IsBrownianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.left","Classical.propDecidable","Continuous","Continuous.comp","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.instZero","ContinuousMap.mk","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","EuclideanSpace","Filter.mp_mem","Filter.univ_mem'","Fintype","GinibrePoincare.bakryEmeryBrownianNoisePath","GinibrePoincare.bakryEmeryBrownianNoiseReal","GinibrePoincare.bakryEmeryBrownianNoiseReal_actual","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NegZeroClass.toZero","Not","OfNat.ofNat","Pi.addCommGroup","Pi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ountableProd","instFintypeProd","instHSMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinCorrectedDriver","name":"GinibrePoincare.bakryEmeryCorrectedCompactDriver","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiff","Continuous","ContinuousMap","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Membership.mem","NNReal","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.mk","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryCorrectedCompactDriver._proof_1","GinibrePoincare.bakryEmeryCorrectedCompactDriver._proof_2","GinibrePoincare.bakryEmeryGibbsConfigurationTilt","GinibrePoincare.bakryEmeryOriginalCompactDriver","GinibrePoincare.configurationEuclideanEquiv","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.instTopologicalSpace","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toSub","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","intervalIntegral"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinCorrectedDriver","name":"GinibrePoincare.bakryEmeryCorrectedCompactDriver._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNe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incare.BakryEmeryHilbertBlock","GinibrePoincare.Configuration","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryBlockHilbertEquiv","GinibrePoincare.bakryEmeryBlockLift","GinibrePoincare.bakryEmeryBlockLift_eq_normalizedGibbs","GinibrePoincare.bakryEmeryBlockLift_squaredRadius","GinibrePoincare.bakryEmeryConfiguration_normalizedGibbs_map","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential.eq_1","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.continuous_gaussianBlockRadius","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.ginibre_configurationEuclidean_norm_sq","GinibrePoincare.potentialSquaredRadiusLaw","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.map_map","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PiLp","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.norm_sq_eq_of_L2","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.continuous_sqrt","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Real.sqrt_sq","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Top.top","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","WithLp","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.ofLp","WithLp.toLp","WithTop.some","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","continuous_const","continuous_norm","eq_self","fact_one_le_two_ennreal","funext","id","instAddNat","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instDecidableEqNat","instDecidableNot","instFintypeProd","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instTopENat","measureSpaceOfInnerPro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rePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LipschitzWith","MeasurableSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","gradient","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","ContDiff","ContDiff.continuous","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryEuclideanLift_gibbs_absolutelyContinuous","GinibrePoincare.bakryEmeryEuclideanLift_gibbs_probability","GinibrePoincare.bakryEmeryEuclideanLift_square_lsi","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.bakryEmery_boundedLipschitz_gradient_lsi_of_compact","HDiv.hDiv","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LipschitzWith","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MetricSpace.toEMetricSpace","NNReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLiftProbability","name":"GinibrePoincare.bakryEmeryEuclideanLift_density_integrable","type_dependencies":["BorelSpace","Complex","Complex.instNormedField","Continuous","FiniteDimensional","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","InnerProductSpac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EuclideanLift_density_integrable","GinibrePoincare.bakryEmeryNormalizedGibbs_probability","InnerProductSpace","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instNeZeroOfNonempty","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddTorsor.toAddTorsor","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instDivisionRing","Real.instLT","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNormedAddTorsor","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_const","continuous_norm","instIsAddHaarMeasureVolume","instIsTopologicalRingReal","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryConvexLift","name":"GinibrePoincare.bakryEmeryEuclideanLift_remainder_convex","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex.ofReal","ConvexOn","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.normedField","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul","Set.univ","SubNegMonoid.toAddMonoid","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And.intro","And.right","Complex.ofReal","Convex","ConvexOn","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Eq","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRadialRemainder","GinibrePoincare.bakryEmeryRadialRemainder_convex","GinibrePoincare.bakryEmeryRadialRemainder_even","GinibrePoincare.even_convex_monotoneOn_nonnegative","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MonotoneOn","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instSub","Real.instZero","Real.normedField","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.instMembership","Set.mem_univ","Set.univ","SubNegMonoid.toAddMonoid","Zero.toOfNat0","add_nonneg","convexOn_univ_norm","convex_univ","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_nonneg","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLiftLSILimit","name":"GinibrePoincare.bakryEmeryEuclideanLift_square_lsi","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","gradient","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.BakryBrownianCoordinateSample","GinibrePoincare.BakryBrownianDyadicCompletedSample","GinibrePoincare.BakryBrownianDyadicIndex","GinibrePoincare.BakryBrownianDyadicSample","GinibrePoincare.BakryBrownianGlobalSample","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryBrownianCoordinateMeasure","GinibrePoincare.bakryBrownianCoordinateProcess","GinibrePoincare.bakryBrownianCoordinate_independent","GinibrePoincare.bakryBrownianCoordinate_isBrownian","GinibrePoincare.bakryBrownianDyadicMeasure","GinibrePoincare.bakryBrownianGlobalMeasure","GinibrePoincare.bakryEmeryEuclideanLift_square_lsi_of_Brownian","GinibrePoincare.instIsCompleteBakryBrownianCoordinateSampleBakryBrownianCoordinateMeasure","GinibrePoincare.instIsProbabilityMeasureBakryBrownianCoordinateSampleBakryBrownianCoordinateMeasure","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure.pi","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLT","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLiftLSILimit","name":"GinibrePoincare.bakryEmeryEuclideanLift_square_lsi_of_Brownian","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","gradient","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddUnits","AddZeroClass.toAddZero","Algebra.id","Algebra.toModule","Algebra.to_smulCommClass","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.instNormedAddCommGroup","ContDiff","ContDiff.continuous","ContDiff.fderiv_right","Continuous","Continuous.comp","Continuous.norm","Continuous.pow","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvMonoid.toDiv","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.refl","Eq.trans","EquivLike.toFunLike","EuclideanSpace","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.mul","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.bakryEmeryRegularizedLift_square_lsi_of_Brownian","GinibrePoincare.bakryEmeryRegularizedLift_volume_entropy_tendsto","GinibrePoincare.bakryEmeryRegularizedLift_volume_expectation_tendsto","GinibrePoincare.squareEntropy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.fderiv","HasSolidNorm.orderClosedTopology","InnerProductSpace.toDual","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsScalarTower.nnrat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.continuous","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.instSemilinearIsometryEquivClass","LinearIsometryEquiv.symm","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","RCLike.toStarRing","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMonoidWit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inibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryEuclideanLift_remainder_convex","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Int","Int.mul","Int.negOfNat","Int.ofNat","Inv.inv","InvOneClass.toInv","IsOrderedModule.toPosSMulMono","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Rat.rawCast","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRing","Real.instSub","Real.linearOrder","Real.normedField","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMul","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","Semiring","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.univ","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","eq_of_heq","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRegularizedLift","name":"GinibrePoincare.bakryEmeryExtraCoordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AffineMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddTorsor.toAddTorsor","NormedCommRing.toSeminormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommGroup","Prod.instModule","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRing","Real.normedCommRing","Real.normedField","Ring.toSemiring","SeminormedAddCommGroup.toNormedAddTorsor","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","WithLp","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdSeminormedAddCommGroup","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toA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oid","Real.instDivInvMonoid","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.semiring","Real.sqrt","Real.toNNReal","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.univ","WithLp.instAddCommGroup","WithLp.instSMul","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instFintypeProd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.left","And.right","Bool","Bool.false","Bool.true","CommMonoid.toMonoid","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","Continuous","Continuous.const_smul","Continuous.continuousOn","ConvexOn","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Dist.dist","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Fintype","Function.hasSMul","GinibrePoincare.bakryEmeryFiniteEndpoint","GinibrePoincare.bakryEmeryLangevinCorrectionOn","GinibrePoincare.bakryEmeryLangevinCorrectionOn_spec","GinibrePoincare.bakryEmeryLangevinDrift","GinibrePoincare.bakryEmeryLangevin_polygonal_noise_response","GinibrePoincare.bakryEmeryPolygonalNoise","GinibrePoincare.bakryEmeryPolygonalNoise_continuous","GinibrePoincare.bakryEmeryResponseCovariance","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasDerivAt","Iff.mp","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","LipschitzWith.of_dist_le_mul","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","NNReal","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommGroup","Pi.instSub","Pi.module","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instNorm","PiLp.instPseudoMetricSpace","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PiLp.uniformSpace","PolynormableSpace.continuousSMul","Preorder.toLE","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.isBoundedSMul","Real.linearOrder","Real.measureSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_nonneg","Real.toNNReal","Real.toNNReal_of_nonneg","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Set","Se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","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toSemiring","ContDiff","Continuous","Continuous.continuousAt","ContinuousAt.tendsto","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousConstSMul","ContinuousMap.instFunLike","ContinuousMap.instSMul","ContinuousMap.mk","ContinuousOn","ConvexOn","DFunLike.coe","Decidable.decide","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.add","Equiv.addCommGroup._proof_1","Equiv.addCommGroup._proof_2","Equiv.injective","Equiv.instEquivLike","Equiv.zero","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.congr'","Filter.Tendsto.const_smul","Filter.Tendsto.prodMk_nhds","Filter.atTop","Fin","Fin.val","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Fintype","Function.Injective.addZeroClass","Function.comp","Function.hasSMul","GinibrePoincare.bakryEmeryFiniteEndpoint","GinibrePoincare.bakryEmeryFiniteEndpoint_sampled_tendsto._proof_1","GinibrePoincare.bakryEmeryLangevinEndpoint","GinibrePoincare.bakryEmeryLangevinEndpoint_continuous","GinibrePoincare.bakryEmeryLangevinEndpoint_eq_finiteEndpoint","GinibrePoincare.bakryEmeryPolygonalNoise","GinibrePoincare.bakryEmeryPolygonalSamplePath","GinibrePoincare.bakryEmeryPolygonalSamplePath_tendsto","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsBoundedSMul.toUniformContinuousConstSMul","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","LT.lt.le","List.nil","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_add","Nat.cast_nonneg'","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NeZero.one","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.addCommGroup","Pi.module","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instNorm","PiLp.instPseudoMetricSpace","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","PiLp.uniformSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMul","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ibrePoincare.bakryEmeryGibbsCompactSurvival","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.instNorm","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival._proof_1","LT.lt","Membership.mem","NNReal","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryEmeryGibbsCompactSurvival._proof_1","type_dependencies":["CompactSpace","Membership.mem","NNReal","NNReal.toReal","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["ConditionallyCompleteLinearOrder.toCompactIccSpace","NNReal","NNReal.toReal","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","instOrderTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryEmeryGibbsCompactSurvival_exhaustion","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.cast","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.iUnion","Set.instMembership","Set.univ","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.instNorm","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","Iff.mpr","LT.lt","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instArchimedean","Real.instConditionallyCompleteLinearOrder","Real.instIsStrictOrderedRing","Real.instNatCast","Real.instPreorder","Real.instZero","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.eq_univ_of_forall","Set.iUnion","Set.instMembership","Set.mem_iUnion","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","exists_nat_gt","instCommCStarAlgebraComplex","instOrderTopologyReal","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryEmeryGibbsCompactSurvival_measurableSet","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","GinibrePoincare.bakryGibbsSurvival_pathMeasurable","MeasurableSet","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.instSeminormedAddCommGroup","DistribLattice.toLattice","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryGibbsSurvival_pathBorel","GinibrePoincare.bakryGibbsSurvival_pathMeasurable","HasSolidNorm.orderClosedTopology","IsOpen.measurableSet","LT.lt","Lattice.toSemilatticeInf","Membership.mem","NNReal","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instIsOrderedAddMonoid","Real.instPreorder","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","continuous_const","continuous_norm","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instHasSolidNormReal","instOrderTopologyReal","instTopologicalSpaceSubtype","isOpen_lt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryEmeryGibbsCompactSurvival_mem","type_dependencies":["CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","Iff","LT.lt","Membership.mem","NNReal","NNReal.toReal","Nat","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedRing.toNorm","OfNat.ofNat","Pi.normedRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["And.intro","CommCStarAlgebra.toNormedCommRing","Complex","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.norm_lt_iff_of_nonempty","Fin","Fin.fintype","GinibrePoincare.Configuration","LE.le","Membership.mem","NNReal","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty.intro","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instLE","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","instCommCStarAlgebraComplex","instOrderTopologyReal","instTopologicalSpaceSubtype","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryEmeryGibbsCompactSurvival_reverse","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.comp","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","GinibrePoincare.ginibreHamiltonianCompactReverseTime","Iff","LE.le","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","ContinuousMap","ContinuousMap.comp","ContinuousMap.instFunLike","DFunLike.coe","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCompactSurvival","GinibrePoincare.bakryEmeryGibbsCompactSurvival_mem","GinibrePoincare.ginibreHamiltonianCompactReverseTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Iff.intro","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedRing.toNorm","OfNat.ofNat","Pi.normedRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instCommSemiring","Real.instLE","Real.instLT","Real.instPreorder","Real.instSub","Real.instZero","Real.pseudoMetricSpace","Ring","Ring.toAddCommGroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.ext","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","inferInstance","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instTopologicalSpaceSubtype","propext","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStopped","name":"GinibrePoincare.bakryEmeryGibbsConfigurationDrift","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instSub","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHMul","instHSub","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStopped","name":"GinibrePoincare.bakryEmeryGibbsConfigurationDrift.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instSub","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configu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Semiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.natCast","WithTop.zero","Zero.toOfNat0","continuous_const","continuous_pi","fderiv","instAddMonoidWithOneENat","instCharZeroENat","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinConfiguration","name":"GinibrePoincare.bakryEmeryGibbsConfigurationDrift_gradient","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.configurationEuclideanEquiv","InnerProductSpace.toNormedSpace","Nat","Neg.neg","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","gradient","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instT2Space","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","ContinuousLinearEquiv","ContinuousLinearEquiv.differentiableAt","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.hasFDerivAt","ContinuousLinearEquiv.symm","ContinuousLinearEquiv.symm_apply_apply","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp.congr_simp","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt","Distrib.toMul","DistribMulAction.toMulAction","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.trans","EquivLike.toFunLike","EuclideanSpace","EuclideanSpace.inner_single_right","EuclideanSpace.single","False.elim","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Fin.mk","Finset","Finset.instSetLike","Fintype.complete","Fintype.elems","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.bakryEmery_configuration_imaginary_single","GinibrePoincare.bakryEmery_configuration_real_single","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.configurationEuclideanEquiv_apply_one","GinibrePoincare.configurationEuclideanEquiv_apply_zero","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSub.hSub","HasFDerivAt.fderiv","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.cons.noConfusion","List.ctorIdx","List.finRange","List.nil","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.le_of_lt","Nat.le_refl","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.t2Space","Pi.topologicalSpace","PiLp.completeSpace","PiLp.ext","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","Prod","Prod.casesOn","Prod.mk","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCompleteSpace","Real.instMul","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomCompTriple.ids","RingHomInvPair.ids","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","Zero.toOfNat0","congr","congrArg","congrFun'","conj_trivial","eq_of_heq","eq_self","fact_one_le_two_ennreal","fderiv","fderiv_comp","gradient","id","inner_gradient_left","instAddNat","instCommCStarAlgebraComplex","instContinuousSMulForall","instDecidableEqFin","instDecidableEqProd","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instTrivialStarReal","neg_zero","noConfusion_of_Nat","of_eq_true","one_mul","starRingEnd","sub_self","sub_zero","zero_add","zero_sub"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"GinibrePoincare.bakryEmeryGibbsConfigurationGradientSq","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instHPow","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"GinibrePoincare.bakryEmeryGibbsConfigurationLaplacian","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instInnerProductSpaceRealComplex"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"GinibrePoincare.bakryEmeryGibbsConfigurationRadialGradient","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instHMul","instInnerProductSpaceRealComplex"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStopped","name":"GinibrePoincare.bakryEmeryGibbsConfigurationTilt","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt","GinibrePoincare.bakryEmeryGibbsRelativePote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urableSpace","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure._proof_1","GinibrePoincare.bakryEmeryGibbsCoordinateWeight","HDiv.hDiv","MeasurableSpace.pi","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemiring","Nat","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","Prod","Real","Real.instZero","Real.measurableSpace","Semiring.toNonAssocSemiring","Zero.toOfNat0","instFintypeProd","instHDiv","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsInitialLaw","name":"GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsInitialLaw","name":"GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure_assembly","type_dependencies":["Algebra.id","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","HDiv.hDiv","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.measurableSpace","Real.normedField","Real.pi","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instHDiv","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","ContDiff.continuous","Continuous","Continuous.measurable","Continuous.mul","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","ENNReal.ofReal_mul","ENat","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure","GinibrePoincare.bakryEmeryGibbsCoordinateRawMeasure._proof_1","GinibrePoincare.bakryEmeryGibbsCoordinateWeight","GinibrePoincare.bakryEmeryGibbsRelativePotential","GinibrePoincare.complexGaussianDensity","GinibrePoincare.complexGaussianDensityIdentification","GinibrePoincare.complexGaussianDensityMeasure","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePo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ric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt._proof_1","GinibrePoincare.ginibreCoordinateDirection","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable.mul","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instCountableFin","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurable_const","measurable_fderiv_apply_const","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStopped","name":"GinibrePoincare.bakryEmeryGibbsPotentialTilt_noise_drift","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt","GinibrePoincare.ginibreCoordinateDirection","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instCommCStarAlgebraComplex","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Bool","Bool.false","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt","GinibrePoincare.bakryEmeryGibbsPotentialTilt._proof_1","GinibrePoincare.ginibreCoordinateDirection","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNRat.rawCast","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","Prod","PseudoMetricSpace.toUniformSpace","Rat.rawCast","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sq_sqrt","Real.sqrt","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","div_nonneg","fderiv","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTransEq","le_of_not_gt","rfl","sq_nonneg"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"GinibrePoincare.bakryEmeryGibbsRelativePotential","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","HMul.hMul","HSub.hSub","Nat","Nat.cast","Real","Real.instMul","Real.instNatCast","Real.instSub","instHMul","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsInitialLaw","name":"GinibrePoincare.bakryEmeryGibbsRelativePotential.eq_1","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsRelativePotential","GinibrePoincare.configurationNormSq","HMul.hMul","HSub.hSub","Nat","Nat.cast","Real","Real.instMul","Real.instNatCast","Real.instSub","instHMul","instHSub"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsRelativePotential","Nat","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsGenerator","name":"GinibrePoincare.bakryEmeryGibbsWeight","type_dependencies":["Real"],"value_dependencies":["Neg.neg","Real","Real.exp","Real.instNeg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsGenerator","name":"GinibrePoincare.bakryEmeryGibbsWeight.eq_1","type_dependencies":["Eq","GinibrePoincare.bakryEmeryGibbsWeight","Neg.neg","Real","Real.exp","Real.instNeg"],"value_dependencies":["Eq.refl","GinibrePoincare.bakryEmeryGibbsWeight","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalCoupling","name":"GinibrePoincare.bakryEmeryGibbs_actual_stopped_coupling","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And.intro","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","ContinuousMap","ContinuousMap.instFunLike","ConvexOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryCorrectedCompactDriver","GinibrePoincare.bakryEmeryGibbsPath","GinibrePoincare.bakryEmeryGibbs_actual_stopped_coupling._proof_1","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreHamiltonianOUReferenceProcess","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Membership.mem","Min.min","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.topologicalSpace","Preorder.toLE","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.norm","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SemilatticeInf.toMin","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Set.univ","Subtype.mk","Subtype.property","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instSMul","WithTop","WithTop.natCast","Zero.toOfNat0","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","Algebra.toSMul","And","And.intro","And.left","And.right","Bool","Bool.false","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","ContDiff","ContDiff.differentiable","Continuous","Continuous.comp","Continuous.const_smul","Continuous.continuousOn","Continuous.intervalIntegrable","ContinuousLinearEquiv","ContinuousLinearEquiv.continuousSemilinearEquivClass","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","ContinuousLinearEquiv.symm_apply_apply","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.intervalIntegral_comp_comm","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.mk","ContinuousSemilinearEquivClass.continuousSemilinearMapClass","ContinuousSemilinearMapClass.toSemilinearMapClass","ConvexOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryCorrectedCompactDriver","GinibrePoincare.bakryEmeryCorrectedCompactDriver._proof_1","GinibrePoincare.bakryEmeryCorrectedCompactDriver.eq_1","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.bakryEmeryGibbsConfigurationDrift_continuous","GinibrePoincare.bakryEmeryGibbsConfigurationTilt","GinibrePoincare.bakryEmeryGibbsConfigurationTilt_continuous","GinibrePoincare.bakryEmeryGibbsConfigurationTilt_eq_drift","GinibrePoincare.bakryEmeryGibbsOU_normalized_equation","GinibrePoincare.bakryEmeryGibbsPath","GinibrePoincare.bakryEmeryGibbsPath_prefix_identification","GinibrePoincare.bakryEmeryOriginalCompactDriver","GinibrePoincare.bkWeightedExtension","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreHamiltonianOUReferenceProcess","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IntervalIntegrable","IsBoundedSMul.toUniformContinuousConstSMul","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toMin","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MeasureTheory.MeasureSpace.volume","Membership.mem","Min.min","Module.toDistribMulAction","Monoid.toNPow","NNReal","NNReal.coe_le_coe._simp_1","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.complete","Pi.instAdd","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.subtractionMonoid","Pi.topologicalSpace","PiLp.completeSpace","PiLp.innerProductSpace._proof_1"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ocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","congrArg","funext","id","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsGenerator","name":"GinibrePoincare.bakryEmeryGibbs_directional_adjoint","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","FiniteDimensional","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsWeight","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instHMul","instHSub","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","BorelSpace","BorelSpace.opensMeasurable","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteSpace","ContDiff","ContDiff.comp","ContDiff.continuous","ContDiff.differentiable","ContDiff.mul","ContDiff.neg","Continuous","Continuous.integrable_of_hasCompactSupport","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.distribMulAction","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.neg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","FiniteDimensional","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.bakryEmeryGibbsWeight.eq_1","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","HasCompactSupport.mul_right","HasFDerivAt","HasFDerivAt.exp","HasFDerivAt.fderiv","HasFDerivAt.mul","HasFDerivAt.neg","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LT.lt","Lattice.toSemilatticeInf","LipschitzAdd.continuousAdd","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tac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are.bakryEmeryLangevinCorrectionOn._proof_1","GinibrePoincare.bakryEmeryLangevinCorrectionOn._proof_2","GinibrePoincare.bakryEmeryLangevinDrift","GinibrePoincare.bakryEmeryLangevin_global_exists_on","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.Ioo","Set.instMembership","Set.univ","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","intervalIntegral"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobal","name":"GinibrePoincare.bakryEmeryLangevinCorrectionOn._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobal","name":"GinibrePoincare.bakryEmeryLangevinCorrectionOn._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobal","name":"GinibrePoincare.bakryEmeryLangevinCorrectionOn.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","ContDiff","Continuous","ConvexOn","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","Eq.ndrec","FiniteDimensional","GinibrePoincare.bakryEmeryLangevinCorrectionOn","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Set.univ","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHDiv","instHMul","instHPow","instHSub","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incare.bakryEmeryLangevinCorrection","GinibrePoincare.bakryEmeryLangevinCorrectionOn","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Set.EqOn","Set.Icc","Set.univ","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And.intro","And.left","And.right","Bool","CommRing.toRing","CommSemiring.toSemiring","CompleteSpace","ContDiff","Continuous","ConvexOn","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","FiniteDimensional","GinibrePoincare.bakryEmeryLangevinCorrectionOn_consistent","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Min.min","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMin","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiri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y","name":"GinibrePoincare.bakryEmeryLangevinDrift.eq_1","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CompleteSpace","Eq","GinibrePoincare.bakryEmeryLangevinDrift","InnerProductSpace","Neg.neg","NegZeroClass.toNeg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","gradient"],"value_dependencies":["CompleteSpace","Eq.refl","GinibrePoincare.bakryEmeryLangevinDrift","InnerProductSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinNoiseStability","name":"GinibrePoincare.bakryEmeryLangevinDrift_closedBall_lipschitz","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CompleteSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.instNatCast","Exists","FiniteDimensional","GinibrePoincare.bakryEmeryLangevinDrift","InnerProductSpace","InnerProductSpace.toNormedSpace","LipschitzOnWith","Metric.closedBall","MetricSpace.toEMetricSpace","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","WithTop","WithTop.natCast","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommSemiring.toSemiring","CompleteSpace","ContDiff","ContDiff.contDiffAt","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiffAt","Continuous","Continuous.continuousOn","Continuous.norm","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.toSeminormedAddCommGroup","Convex.lipschitzOnWith_of_nnnorm_fderiv_le","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.instNatCast","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","FiniteDimensional","FiniteDimensional.proper_real","GinibrePoincare.bakryEmeryLangevinDrift","GinibrePoincare.bakryEmeryLangevinDrift_contDiffAt","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","IsCompact.exists_bound_of_continuousOn","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans","LinearOrder.toMax","LipschitzOnWith","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Max.max","Membership.mem","Metric.closedBall","MetricSpace.toEMetricSpace","NNReal","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Preorder.toLE","ProperSpace.isCompact_closedBall","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMax","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toAddGroupWithOne","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","Set","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","UniformSpace.toTopologicalSpa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eryPolygonalSamplePath_tendsto._proof_1_1","compactSpace_Icc","congrArg","congrFun'","congr_arg\u2082","continuousOn_iff_continuous_restrict","dist_eq_norm","div_one","div_pos","eq_of_heq","eq_self","fact_one_le_two_ennreal","funext","gt_mem_nhds","half_lt_self","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instHSub","instIsCancelMulZero","instLTNat","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instTopologicalSpaceSubtype","le_of_lt","lt_of_le_of_lt","ne_of_gt","nhds","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","tendsto_const_nhds","tendsto_natCast_atTop_atTop"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinCorrectedDriver","name":"GinibrePoincare.bakryEmeryPotentialTilt_time_integral_measurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt","GinibrePoincare.bakryEmeryGibbsRelativePotential","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NNReal.instTopologicalSpace","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.toNNReal","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instCommCStarAlgebraComplex","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.mul","ContDiff.of_le","ContDiff.sub","Continuous","Continuous.comp","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.comp","Function.uncurry","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsPotentialTilt","GinibrePoincare.bakryEmeryGibbsPotentialTilt_continuous","GinibrePoincare.bakryEmeryGibbsPotentialTilt_measurable","GinibrePoincare.bakryEmeryGibbsRelativePotential","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","HEq","HEq.refl","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","Measurable.comp","Measurable.stronglyMeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.StronglyMeasurable","MeasureTheory.StronglyMeasurable.integral_prod_right","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.instSFiniteRestrict","MeasureTheory.integral","MeasureTheory.measurable_uncurry_of_continuous_of_measurable","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.instTopologicalSpace","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","NormedSpace","Not","OfNat.ofNat","OrderTop.toTop","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Prod","Prod.instMeasurableSpace","Prod.swap","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Rea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inibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","HAdd.hAdd","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.integral","MeasureTheory.integral_map","MetricSpace.toEMetricSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","TopologicalSpace.instSecondCountableTopologyForallOfCountable","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","funext","id","instAddNat","instCountableFin","instHAdd","instLTNat","instOfNatNat","instSecondCountableTopologyReal","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLiftTransfer","name":"GinibrePoincare.bakryEmeryProductLift_entropy","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryLiftSquaredRadii","GinibrePoincare.bakryEmeryProductLift","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","GinibrePoincare.squareEntropy","HAdd.hAdd","LT.lt","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous","Continuous.aestronglyMeasurable","Continuous.measurable","Continuous.pow","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mpr","Eq.symm","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryLiftSquaredRadii","GinibrePoincare.bakryEmeryProductLift","GinibrePoincare.bakryEmeryProductLift_squaredRadii","GinibrePoincare.continuous_bakryEmeryLiftSquaredRadii","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","GinibrePoincare.squareEntropy","GinibrePoincare.squareEntropy_map","HAdd.hAdd","HMul.hMul","HPow.hPow","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.borelSpace","Pi.instPow","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instMonoid","Real.instMul","Real.log","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformSpace.toTopologicalSpace","congrArg","id","instAddNat","instCountableFin","instHAdd","instHMul","instHPow","instIsTopologicalRingReal","instLTNat","instOfNatNat","instSecondCountableTopologyReal","secondCountableTopologyEither_of_r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tCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd","Pi.continuousAdd'","Pi.instZero","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.single","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.AlternativeBakryEmeryProductGradient.0.GinibrePoincare.bakryEmeryLiftRadiusDerivative_direction","add_zero","congr","congrArg","congrFun'","fderiv","funext","id","inferInstance","instAddNat","instContinuousSMulForall","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","map_smul","mul_one","one_mul","rfl","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRadialLift","name":"GinibrePoincare.bakryEmeryProductLift_squaredRadii","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryLiftSquaredRadii","GinibrePoincare.bakryEmeryProductLift","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","HAdd.hAdd","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous","Continuous.measurable","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mpr","Eq.trans","Fin","Fin.fintype","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryBlockLift","GinibrePoincare.bakryEmeryBlockLift_isProbabilityMeasure","GinibrePoincare.bakryEmeryBlockLift_squaredRadius","GinibrePoincare.bakryEmeryLiftSquaredRadii","GinibrePoincare.bakryEmeryProductLift","GinibrePoincare.continuous_gaussianBlockRadius","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusLaw","GinibrePoincare.potentialSquaredRadiusProduct","HAdd.hAdd","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi_map_pi","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instCompleteSpace","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","funext","id","instAddNat","instCountableFin","instHAdd","instLTNat","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","of_eq_true","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRadialDrift","name":"GinibrePoincare.bakryEmeryRadialDrift","type_dependencies":["GinibrePoincare.Potential","Nat","Real"],"value_dependencies":["CommSemiring.toSemiring","Complex.ofReal","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","GinibrePoincare.Potential","GinibrePoincare.radialEffectivePotential","Nat","Neg.neg","NontriviallyNormedField.toNormedField","NormedField.toField","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instNeg","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","deriv"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRadialDrift","name":"GinibrePoincare.bakryEmeryRadialDrift_deriv_le","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRadialDrift","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","deriv","instHMul","instInnerProductSpaceRealComplex","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.ofReal","ContDiff","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRadialDrift","GinibrePoincare.radialEffectivePotential","GinibrePoincare.rhoConvexPotential_radial_curvature","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isIn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at","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.instNormedAddCommGroup","Complex.ofReal","ContDiff","ContDiffAt","ContDiffAt.derivWithin","ContDiffAt.differentiableAt","ContinuousAt.continuousWithinAt","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.differentiableWithinAt","DifferentiableAt.hasDerivAt","DifferentiableAt.neg","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRadialDrift","GinibrePoincare.bakryEmeryRadialDrift_deriv_le","GinibrePoincare.contDiffAt_radialEffectivePotential","GinibrePoincare.radialEffectivePotential","HAdd.hAdd","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt","HasDerivAt.add","HasDerivAt.const_mul","HasDerivAt.continuousAt","HasDerivAt.deriv","HasDerivAt.differentiableAt","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsModuleTopology.toContinuousSMul","IsStrictOrderedModule.toPosSMulStrictMono","IsStrictOrderedRing.toIsStrictOrderedModule","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Module","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instAdd","PolynormableSpace.continuousSMul","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpac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ormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq.mp","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean_contDiff","GinibrePoincare.configurationEuclideanEquiv","InnerProductSpace.toNormedSpace","LT.lt","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLT","Real.instRCLike","Real.instRing","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","funext","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRegularizedEuclidean","name":"GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.configurationEuclideanEquiv","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.ofReal","ContinuousLinearEquiv","ContinuousLinearEquiv.apply_symm_apply","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibre_configurationEuclidean_norm_sq","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedCo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oid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","BddAbove","BorelSpace","BorelSpace.opensMeasurable","Complex","Complex.instNormedField","Continuous","Continuous.aestronglyMeasurable","Continuous.bddAbove_range_of_hasCompactSupport","Continuous.norm","DistribLattice.toLattice","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","Exists.casesOn","Filter.Tendsto","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryEuclideanLiftPotential","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.bakryEmeryRegularizedLift_expectation_tendsto","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.norm","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","LE.le","LE.le.trans","Lattice.toSemilatticeInf","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.instZero","MeasureTheory.integral","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.mem_range_self","Set.range","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instClosedIciTopology","instDistribLatticeOfLinearOrder","instHDiv","instHMul","instHPow","instHasSolidNormReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","nhds","norm_nonneg","secondCountableTopologyEither_of_right","upperBounds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRegularizedLift","name":"GinibrePoincare.bakryEmeryRegularizedLift_contDiff","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedLiftPotential","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLT","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","WithTop","WithTop.natCast","Zero.toOfNat0","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","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otential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedLiftPotential","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","OfNat.ofNat","Real","Real.exp","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instZero","Zero.toOfNat0","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instZero","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Even.pow_nonneg","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.bakryEmeryRegularizedLift_quadratic_lower_bound","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toIsOrderedRing","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.neg_subst","Mathlib.Tactic.CancelDenoms.pow_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","Mul","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc",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ormSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","gradient","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.comp","ContinuousLinearEquiv","ContinuousLinearEquiv.contDiff","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","ContinuousLinearEquiv.symm_apply_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq.mp","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.bakryEmeryConfigurationGibbs_square_lsi_of_Brownian","GinibrePoincare.bakryEmeryNormalizedGibbs","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean_contDiff","GinibrePoincare.bakryEmeryRegularizedConfigurationPotential_euclidean_strongConvex","GinibrePoincare.bakryEmeryRegularizedLiftPotential","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","Iff.mpr","InnerProductSpace.toNormedSpace","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Monoid.toNPow","MulZeroClass.toZero","NNReal","NPow.toPow","Nat","Nat.cast","Nat.cast_pos","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonU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orm","name":"GinibrePoincare.bakryEmeryScalarFormGradient","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.BakryEmeryScalarFormAmbient","GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","GinibrePoincare.BakryEmeryScalarL2","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarFormSpace","GinibrePoincare.bakryEmeryScalarMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","ContinuousLinearMap.comp","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.BakryEmeryScalarFormAmbient","GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","GinibrePoincare.BakryEmeryScalarL2","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarFormSpace","GinibrePoincare.bakryEmeryScalarFormSpace._proof_1","GinibrePoincare.bakryEmeryScalarFormSpace._proof_2","GinibrePoincare.bakryEmeryScalarFormValue._proof_1","GinibrePoincare.bakryEmeryScalarMeasure","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.subtypeL","Subtype","UniformSpace.toTopologicalSpace","WithLp","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","WithLp.sndL","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.bakryEmeryScalarFormResolvent","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.BakryEmeryScalarFormAmbient","GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","GinibrePoincare.BakryEmeryScalarL2","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarFormSpace","GinibrePoincare.bakryEmeryScalarMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","M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qFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommGroup","Prod.instModule","Prod.isScalarTower","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SemilinearIsometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","StrongDual","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instIsScalarTower","WithLp.instModule","WithLp.instProdInnerProductSpace","WithLp.instProdNormedAddCommGroup","WithLp.instProdNormedSpace","WithLp.instProdSeminormedAddCommGroup","WithLp.instProdTopologicalSpace","congr","congrArg","congrFun'","eq_of_heq","eq_self","fact_one_le_two_ennreal","heq_of_eq","id","innerSL","instHMul","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instSMulOfMul","instTopologicalSpaceSubtype","map_smul","of_eq_true","smul_apply","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryScalarForm","name":"GinibrePoincare.bakryEmeryScalarFormResolventLinear.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","GinibrePoincare.BakryEmeryScalarFormAmbient","GinibrePoincare.BakryEmeryScalarFormAmbient._proof_1","GinibrePoincare.BakryEmeryScalarL2","GinibrePoincare.BakryEmeryScalarL2._proof_1","GinibrePoincare.bakryEmeryScalarFormResolvent","GinibrePoincare.bakryEmeryScalarFormResolventLinear","GinibrePoincare.bakryEmeryScalarFormResolventLinear._proof_1","GinibrePoincare.bakryEmeryScalarFormResolventLinear._proof_2","GinibrePoincare.bakryEmeryScalarFormSpace","GinibrePoincare.bakryEmeryScalarFormSpace._proof_1","GinibrePoincare.bakryEmeryScalarFormSpace._proof_2","GinibrePoincare.bakryEmeryScalarMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.mk","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRin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iv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddTorsor.nonempty","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CompleteSpace","ContDiff","ContDiff.continuous","ConvexOn","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","FiniteDimensional","GinibrePoincare.bakryEmeryNormalizedGibbs_probability","GinibrePoincare.bakryEmeryStrongConvex_density_integrable","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instNeZeroOfNonempty","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddTorsor.toAddTorsor","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNormedAddTorsor","SeminormedAddCommGroup.toPseudoMetricSpace","Set.univ","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHDiv","instHMul","instHPow","instHSub","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsInitialLawMass","name":"GinibrePoincare.bakryEmeryStrongConvex_quadratic_lower_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CommSemiring.toSemiring","CompleteSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ConvexOn","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Field.toSemifield","FiniteDimensional","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set.univ","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fderiv","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toNatModule","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAdd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,"Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformContinuous","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_sub","congrArg","id","inferInstance","instCountableNat","instDiscreteTopologyNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsCountablyGenerated_atTop","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceNat","le_of_not_gt","nhds","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGradientBasis","name":"GinibrePoincare.bakryEmery_directionalEnergy_orthonormalBasis","type_dependencies":["CompleteSpace","DFunLike.coe","Eq","Fintype","GinibrePoincare.directionalEnergy","HPow.hPow","InnerProductSpace","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace","gradient","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DivisionRing.toRing","Eq","Eq.mpr","Eq.symm","Eq.trans","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Finset.sum","Finset.univ","Fintype","GinibrePoincare.directionalEnergy","HPow.hPow","InnerProductSpace","InnerProductSpace.toDual","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.apply_symm_apply","LinearIsometryEquiv.instEquivLike","Monoid.toNPow","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","OrthonormalBasis.sum_sq_inner_left","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StrongDual","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fderiv","gradient","id","instDistribOfSemiring","instHPow","instOfNatNat","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyFlow","name":"GinibrePoincare.bakryEmery_entropyFlow_bound","type_dependencies":["CommSemiring.toSemiring","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DivInvMonoid.toDiv","Field.toSemifield","Filter.Tendsto","Filter.atTop","HDiv.hDiv","HMul.hMul","HasDerivAt","LE.le","LT.lt","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set.Ici","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousOn","ContinuousOn.div_const","ContinuousOn.sub","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.differentiableWithinAt","DifferentiableAt.hasDerivAt","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.div_const","Filter.Tendsto.sub","Filter.atTop","Filter.atTop_neBot","Filter.eventually_ge_atTop","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt","HasDerivAt.deriv","HasDerivAt.differentiableAt","HasDerivAt.div_const","HasDerivAt.sub","HasSolidNorm.orderClosedTopology","Iff.mp","Int","Int.instDecidableEq","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddRightMono","IsOrderedModule.toPosSMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","LE.le.trans_eq","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","LinearOrderedSemiField.toDenselyOrdered","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.neg_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonotoneOn","Mul","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNRat.rawCast","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NeZero.one","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instSub","PolynormableSpace.continuousSMul","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat.rawCast","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instArchimedean","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInhabited","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.Ioi","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyFlow.0.GinibrePoincare.bakryEmery_entropyFlow_bound._simp_1_1","congrArg","congrFun'","congr_arg","congr_arg\u2082","convex_Ici","deriv","div_le_div_of_nonneg_right","div_one","eq_self","ge_of_tendsto","id","inferInstance","instClosedIciTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsCancelMulZero","instIsDirectedOrder","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNoMinOrderOfNontrivial","instNonemptyOfInhabited","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instPolynormableSpace","interior","interior_Ici","le_of_lt","le_of_not_gt","monotoneOn_of_deriv_nonneg","mul_neg","mul_one","mul_pos","ne_of_gt","neg_div","neg_mul","nhds","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","sub_nonpos","sub_self","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BakryEmeryRegularizationVolume","name":"GinibrePoincare.bakryEmery_gaussian_majorant_integrable","type_dependencies":["BorelSpace","FiniteDimensional","HMul.hMul","HPow.hPow","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHPow","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAdd","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddZero.mk","AddZeroClass.toAddZero","BorelSpace","CommRing.toNonUnitalCommRing","CommRing.toRing","Complex","Complex.addGroupWithOne","Complex.exp","Complex.exp_ofReal_re","Complex.instAdd","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.ofReal_mul","Complex.ofReal_neg","Complex.ofReal_pow","Complex.re","ContinuousENorm","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","FiniteDimensional","GaussianFourier.integrable_cexp_neg_mul_sq_norm_add","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HasDistribNeg.toInvolutiveNeg","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","LT.lt","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.re","MeasureTheory.Measure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","MulZeroClass.toZero","MulZeroClass.zero_mul","NPow.toPow","Nat","Neg.neg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.re","RCLike.toDenselyNormedField","Real","Real.commRing","Real.exp","Real.instAddMonoid","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","autoParam","congr","congrArg","eq_of_heq","funext","id","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatNat","measureSpaceOfInnerProductSpace","neg_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BakryEmeryDirectionalCurvature","name":"GinibrePoincare.bakryEmery_gradient_strong_monotonicity","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ConvexOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Field.toSemifield","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.univ","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","fderiv","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoid.toNatModule","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.module","ContinuousLinearMap.sub","ContinuousLinearMap.topologicalSpace","ContinuousSemilinearMapClass.toSemilinearMapClass","ConvexOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.metrizableSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.bakryEmery_convex_support","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasFDerivAt","HasFDerivAt.const_mul","HasFDerivAt.differentiableAt","HasFDerivAt.fderiv","HasFDerivAt.sub","HasStrictFDerivAt.hasFDerivAt","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib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","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsBotZeroClass","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","le_of_lt","mul_pos","pseudoEMetricSpacePi","zero_le"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRadiusLaw","name":"GinibrePoincare.bakryEmery_radius_gradient_energy","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CommSemiring.toSemiring","CompleteSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","HPow.hPow","InnerProductSpace","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Ne","NegZeroClass.toZero","Nontrivial","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","deriv","gradient","instHPow","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","ContDiff","ContDiff.differentiable","ContDiffAt.differentiableAt","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.module","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt","DifferentiableAt.hasDerivAt","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","Eq","Eq.trans","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Function.comp","HMul.hMul","HPow.hPow","HSMul.hSMul","HasDerivAt.comp_hasFDerivAt","HasFDerivAt","HasFDerivAt.fderiv","HasGradientAtFilter._proof_1","HasGradientAtFilter._proof_2","HasGradientAtFilter._proof_3","HasGradientAtFilter._proof_4","HasGradientAtFilter._proof_5","InnerProductSpace","InnerProductSpace.toDual","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.norm_map","LinearIsometryEquiv.symm","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toNPow","MulZeroClass.toMul","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Ne","NeZero.charZero_one","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nontrivial","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","RCLike.toStarRing","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instOne","Real.instRCLike","Real.instRing","Real.lattice","Real.linearOrder","Real.metricSpace","Real.norm","Real.norm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ometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StarOrderedRing.toIsOrderedRing","StrongDual","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformContinuous","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.one","WithTop.zero","Zero.toOfNat0","abs","congr","congrArg","congrFun'","eq_self","fderiv","gradient","instAddENat","instAddMonoidWithOneENat","instArchimedeanNat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHasSolidNormReal","instInhabitedNat","instIsDirectedOrder","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNonemptyOfInhabited","instNontrivialENat","instOfNatNat","instOneENat","instZeroENat","le_of_tendsto_of_tendsto'","map_zero","nhds","norm_zero","not_false_eq_true","of_eq_true","smulCommClass_self","starRingEnd","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsLSIContraction","name":"GinibrePoincare.bakryEmery_uniformObservable_difference_tendsto","type_dependencies":["Dist.dist","Filter.Tendsto","Filter.atTop","HSub.hSub","Nat","Nat.instPreorder","OfNat.ofNat","PseudoMetricSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.instSub","Real.instZero","Real.pseudoMetricSpace","UniformContinuous","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHSub","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","And","And.casesOn","Dist.dist","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Filter.Eventually","Filter.Tendsto","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","GT.gt","HSub.hSub","Iff.mp","IsOrderedAddMonoid.toAddLeftMono","LT.lt","Membership.mem","Metric.tendsto_nhds","Metric.uniformContinuous_iff","Nat","Nat.instPreorder","OfNat.ofNat","PseudoMetricSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLT","Real.instPreorder","Real.instSub","Real.instZero","Real.lattice","Real.pseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuous","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","congrFun'","dist_nonneg","id","instHSub","nhds","propext","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryRadialLift","name":"GinibrePoincare.bakryEmery_volume_squaredBlockRadius","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.radialPowerMeasure","HMul.hMul","HSMul.hSMul","IsScalarTower.right","LT.lt","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.measurableSpace","Set","Set.Iic","Set.preimage","instDistribOfSemiring","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Bool","Bool.true","BorelSpace.opensMeasurable","CommMagma.toMul","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.finrank_real_complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.normSq","Complex.normSq_eq_norm_sq","Complex.normSq_eq_zero","Complex.normSq_nonneg","Continuous.measurable","ContinuousAdd.measurableAdd","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionSemiring.toGroupWithZero","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instZero","ENNReal.ofReal","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Fin.mk","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","Finset","Finset.card","Finset.instSetLike","Finset.mem_univ","Finset.single_le_sum","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.sum_const_zero","Finset.sum_eq_zero_iff_of_nonneg","Finset.univ","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.hasSMul","Function.swap","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.configurationNormSq_nonneg","GinibrePoincare.configurationNormSq_real_smul","GinibrePoincare.continuous_gaussianBlockRadius","GinibrePoincare.gaussianBlockRadius","GinibrePoincare.map_quadratic_homogeneous_measure","GroupWithZero.toNoZeroSMulDivisors","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff","Iff.intro","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact","IsCompact.measure_lt_top","IsCompact.of_isClosed_subset","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","LT.lt.ne'","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.natCast_nonneg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Ma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ocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.uniqueOfIsEmpty","Preorder.toLE","Preorder.toLT","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.log","Real.log_pow","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.univ","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Subsingleton.elim","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","Zero.toOfNat0","abs","congr","congrArg","congrFun'","funext","id","inferInstance","instAddNat","instClosedIciTopology","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instHasSolidNormReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instReflLe","le_of_not_gt","measurable_prodMk_left","of_eq_true","one_mul","rfl","sub_self"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyPiTensorization","name":"GinibrePoincare.bakryEntropyPiCoordinate","type_dependencies":["DecidableEq","MeasurableSpace","MeasureTheory.Measure","Real"],"value_dependencies":["DecidableEq","Function.update","GinibrePoincare.squareEntropy","MeasurableSpace","MeasureTheory.Measure","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyPiTensorization","name":"GinibrePoincare.bakryEntropyPiCoordinate.congr_simp","type_dependencies":["DecidableEq","Eq","GinibrePoincare.bakryEntropyPiCoordinate","MeasurableSpace","MeasureTheory.Measure","Real"],"value_dependencies":["Decidable","DecidableEq","Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.bakryEntropyPiCoordinate","MeasurableSpace","MeasureTheory.Measure","Pi.instSubsingleton","Real","Subsingleton.elim","instSubsingletonDecidable"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyPiTensorization","name":"GinibrePoincare.bakryEntropyPiCoordinate.eq_1","type_dependencies":["DecidableEq","Eq","Function.update","GinibrePoincare.bakryEntropyPiCoordinate","GinibrePoincare.squareEntropy","MeasurableSpace","MeasureTheory.Measure","Real"],"value_dependencies":["DecidableEq","Eq.refl","GinibrePoincare.bakryEntropyPiCoordinate","MeasurableSpace","MeasureTheory.Measure","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryEntropyPiTensorization","name":"GinibrePoincare.bakryEntropyPiCoordinate_integrable","type_dependencies":["DecidableEq","Fintype","GinibrePoincare.bakryEntropyPiCoordinate","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.pi","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.instZero","Real.lattice","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs"],"value_dependencies":["DecidableEq","Fintype","Function.update","GinibrePoincare.bakryEntropy_fiber_integrable_bounded","LE.le","Measurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.Mea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ormSpace.toTopologicalSpace","instCommCStarAlgebraComplex","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"GinibrePoincare.bakryGibbsReversal_fullMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","borel","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStationaryReference","name":"GinibrePoincare.bakryGibbsStationaryReference_pathBorel","type_dependencies":["BorelSpace","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryGibbsStationaryReference_pathMeasurable","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.mk","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryGibbsStationaryReference_pathMeasurable","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalStationaryReference","name":"GinibrePoincare.bakryGibbsStationaryReference_pathMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalSurvival","name":"GinibrePoincare.bakryGibbsSurvival_pathBorel","type_dependencies":["BorelSpace","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryGibbsSurvival_pathMeasurable","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.mk","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","Ginibr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BakryEmeryRadialProductAssembly","name":"GinibrePoincare.bakryRadius_update_lipschitz","type_dependencies":["DecidableEq","EMetricSpace.toPseudoEMetricSpace","Fintype","Function.update","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","NNReal.instOne","OfNat.ofNat","One.toOfNat1","Real","Real.metricSpace","pseudoEMetricSpacePi"],"value_dependencies":["DecidableEq","Dist.dist","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","Fintype","Function.update","Function.update_of_ne","Function.update_self","HMul.hMul","Iff.mpr","LE.le","LipschitzWith.of_dist_le_mul","MetricSpace.toPseudoMetricSpace","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instOne","NNReal.toReal","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toDist","Real","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Real.metricSpace","Real.pseudoMetricSpace","Real.semiring","Std.le_refl._simp_1","True","Zero.toOfNat0","congr","congrArg","congrFun'","dist_nonneg","dist_nonneg._simp_1","dist_pi_le_iff","dist_self","dite","id","instHMul","instMulZeroOneClassOfSemiring","instReflLe","of_eq_true","one_mul","pseudoMetricSpacePi"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsStationaryLaw","name":"GinibrePoincare.bakryStationaryLaw_configBorel","type_dependencies":["BorelSpace","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryStationaryLaw_configMeasurable","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.mk","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.bakryStationaryLaw_configMeasurable","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsStationaryLaw","name":"GinibrePoincare.bakryStationaryLaw_configMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsStationaryLaw","name":"GinibrePoincare.bakryStationaryLaw_euclideanBorel","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","ContinuousMap","ContinuousMap.compactOpen","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","GinibrePoincare.bakryStationaryLaw_euclideanMeasurable","Membership.mem","NNReal","NNReal.toReal","Nat","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.mk","ContinuousMap","ContinuousMap.compactOpe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ul","Real.instNatCast","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toMonoid","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","inner_self_eq_norm_sq_to_K","inner_sum","instDecidableEqFin","instHAdd","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_left_of_eq_true","of_eq_true","sum_inner"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBochnerKodairaCompact","name":"GinibrePoincare.bkCompact_number_pair","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instAdd","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.BKCompactTest","GinibrePoincare.BKCompactTest.adjoint","GinibrePoincare.BKCompactTest.dbar","GinibrePoincare.BKCompactTest.l2","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HAdd.hAdd","HMul.hMul","HPow.hPow","Inner.inner","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instDecidableEqFin","instHAdd","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","ite"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.BKCompactTest","GinibrePoincare.BKCompactTest.adjoint","GinibrePoincare.BKCompactTest.dbar","GinibrePoincare.BKCompactTest.l2","GinibrePoincare.Configuration","GinibrePoincare.bkCompact_adjoint_pairing","GinibrePoincare.bkCompact_adjoint_pairing_right","GinibrePoincare.bkCompact_commutator","GinibrePoincare.bkCompact_dbar_comm","GinibrePoincare.complexGaussianMeasure","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnital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oup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instT2Space","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.distribMulAction","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bkDirectional","GinibrePoincare.bkDirectional_contDiff","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HasFDerivAt","HasFDerivAt.add","HasFDerivAt.const_mul","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.s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ativeBochnerKodairaIdentity","name":"GinibrePoincare.bkGaussian_integrated_identity","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","GinibrePoincare.gaussianDbarAdjointTest","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_add","Complex.ofReal_inj._simp_1","Complex.ofReal_mul","Complex.ofReal_pow","Complex.ofReal_pow._simp_1","Complex.ofReal_sum","ContDiff","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","Fin.fintype","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.mul_sum","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.sum_ite_eq","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.bkGaussian_number_pair","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.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ul.hMul","HSub.hSub","Nat","OfNat.ofNat","One.toOfNat1","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBochnerKodairaDifferential","name":"GinibrePoincare.bkPartial._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBochnerKodairaDifferential","name":"GinibrePoincare.bkPartial_contDiff","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.I","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSub","ContDiff","ContDiff.mul","ContDiff.sub","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bkDirectional","GinibrePoincare.bkDirectional_contDiff","GinibrePoincare.bkPartial._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","contDiff_const","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBochnerKodairaDifferential","name":"GinibrePoincare.bkPartial_eq_conj_dbar","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instNormedField","Complex.instStarRing","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.dbarComponent","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Algebra.toModule","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.conjCLE","Complex.conj_I","Complex.div_ofNat_im","Complex.div_ofNat_re","Complex.ext","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Comp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ommMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianRadialLift","name":"GinibrePoincare.blockRadiusDerivative._proof_1","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianRadialLift","name":"GinibrePoincare.blockRadiusDerivative._proof_2","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","Distrib.toMul","Real","Real.instCommSemiring","SMulCommClass","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommSemiring.toSemiring","Real","Real.instCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianRadialLift","name":"GinibrePoincare.blockRadiusDerivative._proof_3","type_dependencies":["ContinuousConstSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instMul","Real.pseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianRadialLift","name":"GinibrePoincare.blockRadiusDerivative._proof_4","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianRadialLift","name":"GinibrePoincare.blockRadiusDerivative.eq_1","type_dependencies":["CommRing.toNonUnitalCommRing","Complex","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedField","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","Eq","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockCoordinateProjection","GinibrePoincare.blockCoordinateProjection._proof_1","GinibrePoincare.blockRadiusDerivative","GinibrePoincare.blockRadiusDerivative._proof_1","GinibrePoincare.blockRadiusDerivative._proof_2","GinibrePoincare.blockRadiusDerivative._proof_3","GinibrePoincare.blockRadiusDerivative._proof_4","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Eq.refl","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockRadiusDerivative","HAdd.hAdd","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator","name":"GinibrePoincare.bochnerCoordinateOperator","type_dependencies":["Fintype","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"],"value_dependencies":["Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerDirectionalDerivative","HMul.hMul","HSub.hSub","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","Real.normedField","instHMul","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerCoordinateOperator_const_mul","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fintype","GinibrePoincare.bochnerCoordinateOperator","HMul.hMul","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instHMul","instTopENat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","Fintype","GinibrePoincare.bochnerCoordinateOperator","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_const_mul","GinibrePoincare.bochnerDirectionalDerivative_contDiff","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Mathlib.Tactic.RingNF.add_assoc_rev","Mathlib.Tactic.RingNF.add_neg","Mathlib.Tactic.RingNF.int_rawCast_neg","Mathlib.Tactic.RingNF.mul_assoc_rev","Mathlib.Tactic.RingNF.mul_neg","Mathlib.Tactic.RingNF.nat_rawCast_1","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemirin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at.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Not","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator.0.GinibrePoincare.bochnerCoordinateOperator_mul_at._simp_1_1","_private.GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator.0.GinibrePoincare.bochnerCoordinateOperator_mul_at._simp_1_2","add_zero","congr","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instZeroENat","mul_add","mul_one","not_false_eq_true","of_eq_true","pow_one","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerCoordinateOperator_sum","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerCoordinateOperator","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CommRing.toNonUnitalCommRing","ContDiff","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.trans","False","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_comm","Finset.sum_congr","Finset.sum_sub_distrib","Finset.univ","Fintype","GinibrePoincare.bochnerCoordinateOperator","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_contDiff","GinibrePoincare.bochnerDirectionalDerivative_sum","HMul.hMul","HSub","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Not","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedField","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Top.top","True","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun","congrFun'","funext","id","instHMul","instHSub","instTopENat","instZeroENat","not_false_eq_true","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative","type_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGeneratorGradientCommutation","name":"GinibrePoincare.bochnerDirectionalDerivative.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv"],"value_dependencies":["Eq.refl","GinibrePoincare.bochnerDirectionalDerivative","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_add","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHAdd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Eq.mpr","Eq.refl","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.toContinuousAdd","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","congrArg","fderiv","fderiv_fun_add","id","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_comm","type_dependencies":["ContDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiffAt","ContDiffAt.isSymmSndFDerivAt","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.trans","False","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_iterated","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsSymmSndFDerivAt.eq","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.natCast","WithTop.ofNat_ne_top._simp_1","WithTop.some","WithTop.top","congrArg","congrFun'","fderiv","id","instAddMonoidWithOneENat","instIsRCLikeNormedField","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instOrderTopENat","instPreorderENat","instTopENat","minSmoothness","minSmoothness_of_isRCLikeNormedField","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_const_mul","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HMul.hMul","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.to_smulCommClass","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HMul.hMul","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","congrArg","fderiv","fderiv_const_mul","id","instDistribOfSemiring","instHMul","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_contDiff","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["ContDiff","ContDiff.clm_apply","ContDiff.fderiv_right","DenselyNormedField.toNontriviallyNormedField","ENat","InnerProductSpace.toNormedSpace","LE.le","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Std.le_refl._simp_1","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","contDiff_const","fderiv","instPreorderENat","instReflLe","instTopENat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_contDiffAt","type_dependencies":["ContDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["ContDiffAt","ContDiffAt.clm_apply","ContDiffAt.fderiv_right","DenselyNormedField.toNontriviallyNormedField","ENat","InnerProductSpace.toNormedSpace","LE.le","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Std.le_refl._simp_1","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","contDiffAt_const","fderiv","instPreorderENat","instReflLe","instTopENat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_iterated","type_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiffAt","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiffAt","ContDiffAt.differentiableAt","ContDiffAt.fderiv_right","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.comp.congr_simp","ContinuousLinearMap.comp_zero","ContinuousLinearMap.flip","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.topologicalSpace","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","Pi.instZero","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Std.le_refl._simp_1","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun","congrFun'","differentiableAt_const","eq_self","fderiv","fderiv_clm_apply","fderiv_fun_const","id","instHAdd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instPreorderENat","instReflLe","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","smulCommClass_self","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_mul","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","HMul.hMul","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHAdd","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","fderiv_fun_mul","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instMulZeroClassOfSemiring","instSMulOfMul","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator","name":"GinibrePoincare.bochnerDirectionalDerivative_second_mul","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTopENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.mul","Distrib.toAdd","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_add","GinibrePoincare.bochnerDirectionalDerivative_contDiff","GinibrePoincare.bochnerDirectionalDerivative_mul","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedSpace","Not","OfNat.ofNat","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instCommSemiring","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Ring.toAddGroupWithOne","Semiring.toMonoid","Semiring.toNonAssocSemiring","Top.top","True","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator","name":"GinibrePoincare.bochnerDirectionalDerivative_second_mul_at","type_dependencies":["ContDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bochnerDirectionalDerivative","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContDiffAt","ContDiffAt.differentiableAt","ContDiffAt.eventually","ContDiffAt.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.mul","Distrib.toAdd","Distrib.toMul","ENat","ENat.top_ne_one._simp_1","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.EventuallyEq.fderiv_eq","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_add","GinibrePoincare.bochnerDirectionalDerivative_contDiffAt","GinibrePoincare.bochnerDirectionalDerivative_mul","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_eq_coe._simp_2","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","congrArg","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","instZeroENat","nhds","not_false_eq_true","of_eq_true","one_ne_zero._simp_1","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_sub","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HSub.hSub","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instSub","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.sub","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DivisionRing.toRing","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.bochnerDirectionalDerivative","HSub.hSub","InnerProductSpace.toNormedSpace","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","congrArg","fderiv","fderiv_fun_sub","id","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","name":"GinibrePoincare.bochnerDirectionalDerivative_sum","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Field.toSemifield","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerDirectionalDerivative","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsZeroApply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Finset","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.toContinuousAdd","Membership.mem","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fderiv","fderiv_fun_sum","id","of_eq_true","sum_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator","name":"GinibrePoincare.bochnerDirectionalDerivative_third_comm","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bochnerDirectionalDerivative","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["ContDiff","ContDiff.contDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.mpr","Eq.refl","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_comm","GinibrePoincare.bochnerDirectionalDerivative_contDiff","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","congrArg","funext","id","instTopENat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerGamma","type_dependencies":["Fintype","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"],"value_dependencies":["DivInvMonoid.toDiv","Fintype","GinibrePoincare.bochnerCoordinateOperator","GinibrePoincare.bochnerGamma._proof_1","HDiv.hDiv","HMul.hMul","HSub.hSub","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.normedField","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerGamma._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerGammaTwo","type_dependencies":["Fintype","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"],"value_dependencies":["DivInvMonoid.toDiv","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerCoordinateOperator","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerGamma._proof_1","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.normedField","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","name":"GinibrePoincare.bochnerGammaTwo_eq","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","ENat","Eq","Field.toSemifield","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerGammaTwo","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instHAdd","instHMul","instHPow","instOfNatNat","instTopENat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.pow","ContDiff.sum","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.sum_sub_distrib","Finset.univ","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.bochnerCoordinateOperator","GinibrePoincare.bochnerCoordinateOperator_const_mul","GinibrePoincare.bochnerCoordinateOperator_directional_commutation","GinibrePoincare.bochnerCoordinateOperator_mul","GinibrePoincare.bochnerCoordinateOperator_sum","GinibrePoincare.bochnerDirectionalDerivative","GinibrePoincare.bochnerDirectionalDerivative_contDiff","GinibrePoincare.bochnerGamma._proof_1","GinibrePoincare.bochnerGammaTwo","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.No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omplex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","EuclideanSpace","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGaussianSchwartzDbar","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.bochnerKodaira_ginibre_weak_first_deficit","GinibrePoincare.gaussianSchwartzDbar_iff_weak","GinibrePoincare.ginibreDifferentialDeficitVector","GinibrePoincare.ginibreDifferentialDeficit_weak_derivatives","GinibrePoincare.ginibreDifferentialFirstDerivative","GinibrePoincare.ginibreDifferentialSecondDerivative","GinibrePoincare.ginibreDifferentialSecondEnergy","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreGenerator_second_deficit_algebra","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.ginibreWeakEnergy","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddComm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CommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Algebra.id","And.intro","And.right","Bool","Bool.false","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiffBump.contDiff_normed","ContDiffBump.convolution_tendsto_right_of_continuous","ContDiffBump.hasCompactSupport_normed","ContDiffBump.normed","Continuous","Continuous.aestronglyMeasurable","Continuous.clm_apply","Continuous.locallyIntegrable","Continuous.measurable","Continuous.pow","Continuous.tendsto","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.lsmul","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.topologicalSpace","ContinuousMul.measurableMul\u2082","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.const_mul","Filter.Tendsto.pow","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional","FiniteDimensional.proper_real","Finset","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","Function.swap","GinibrePoincare.ae_fderiv_mollification_tendsto","GinibrePoincare.directionalEnergy","GinibrePoincare.integrable_mul_log_of_bounded_nonneg","GinibrePoincare.lsiMollifier","GinibrePoincare.lsiMollifier_radius_tendsto","GinibrePoincare.norm_fderiv_mollification_le","GinibrePoincare.squareEntropy","GinibrePoincare.squareEntropy_le_of_ae_tendsto","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport.contDiff_convolution_left","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","LipschitzWith","LipschitzWith.continuous","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.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lier","name":"GinibrePoincare.boundedMultiplierLinearMap_bound","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","GinibrePoincare.boundedMultiplierLinearMap","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","LinearMap.instFunLike","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instLE","Real.instMul","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.boundedMultiplierLinearMap","GinibrePoincare.boundedMultiplier_memLp","HMul.hMul","InnerProductSpace.toNormedSpace","IsOrderedRing.toMulPosMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","LinearMap.instFunLike","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Real.partialOrd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NormedField.toNontriviallyNormedField","Filter","Filter.Tendsto","IsClosed","LE.le","NNNorm.nnnorm","NNReal","NNReal.instPartialOrder","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomIsometric.ids","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","Set.ofPred","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lipschitz","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Equicontinuous.isClosed_setOfPred_tendsto","Field.toSemifield","Filter","LE.le","LipschitzWith.uniformEquicontinuous","LipschitzWith.weaken","NNNorm.nnnorm","NNReal","NNReal.instPartialOrder","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","PartialOrder.toPreorder","Preorder.toLE","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","UniformEquicontinuous.equicontinuous","UniformSpace.toTopologicalSpace","continuous_id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionLaplaceFubini","name":"GinibrePoincare.boundedTransitionMean_laplace_fubini","type_dependencies":["Eq","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.SFinite","MeasureTheory.integral","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousMul.measurableMul\u2082","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","FiniteDimensional.rclike_to_real","Function.comp","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","Measurable.mul","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.comp_snd","MeasureTheory.AEStronglyMeasurable.mul","MeasureTheory.Integrable","MeasureTheory.Integrable.aestronglyMeasurable","MeasureTheory.Integrable.mono'","MeasureTheory.Integrable.mul_const","MeasureTheory.Integrable.mul_prod","MeasureTheory.Integrable.norm","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.SFinite","MeasureTheory.ae_of_all","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.instSFiniteRestrict","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const_mul","MeasureTheory.integral_integral_swap","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","NormedRing.toRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measurable_exp","Real.measureSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set.Ioi","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_pos","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsAddHaarMeasureVolume","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instProperSpaceReal","instSecondCountableTopologyReal","instTransEq_1","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","integrableOn_exp_mul_Ioi","locallyCompact_of_proper","lt_of_not_ge","measurable_const","measurable_fst","mul_le_mul_of_nonneg_left","norm_mul","norm_nonneg","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianGridComparison","name":"GinibrePoincare.brownianActualLeftGridSum","type_dependencies":["NNReal","Nat","Real"],"value_dependencies":["Finset.range","Finset.sum","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianShiftedLimit","name":"GinibrePoincare.brownianActualLeftGridSum.eq_1","type_dependencies":["Eq","Finset.range","Finset.sum","GinibrePoincare.brownianActualLeftGridSum","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.brownianActualLeftGridSum","NNReal","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianConcatenatedGrid","name":"GinibrePoincare.brownianActualLeftGridSum_concatenated","type_dependencies":["Distrib.toAdd","Eq","Finset.range","Finset.sum","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.itoConcatenatedGrid","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","NNReal","NNReal.instSemiring","Nat","OfNat.ofNat","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Decidable.byContradiction","Distrib.toAdd","Eq","Eq.mpr","Eq.rec","Eq.refl","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.sum","Finset.sum_congr","Finset.sum_range_add","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.itoConcatenatedGrid","GinibrePoincare.itoConcatenatedGrid_first","GinibrePoincare.itoConcatenatedGrid_second","GinibrePoincare.itoUniformNNTime","HAdd","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","LE.le","LT.lt","LT.lt.le","Membership.mem","NNReal","NNReal.instSemiring","Nat","Nat.decLe","Nat.instPreorder","Not","OfNat.ofNat","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instSub","SetLike.instMembership","_private.GinibrePoincare.Analysis.BrownianIntegralGaussianConcatenatedGrid.0.GinibrePoincare.brownianActualLeftGridSum_concatenated._proof_1_1","_private.GinibrePoincare.Analysis.BrownianIntegralGaussianConcatenatedGrid.0.GinibrePoincare.brownianActualLeftGridSum_concatenated._proof_1_2","congrArg","id","instAddNat","instDecidableEqNat","instDistribOfSemiring","instHAdd","instHMul","instHSub","instLENat","instLTNat","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianGridComparison","name":"GinibrePoincare.brownianActualLeftGridSum_difference_tendsto_meanSquare","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ContinuousOn","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fintype","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","And.left","And.right","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommRing.toNonUnitalCommRing","CommRing.toRi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","Filter.Eventually.of_forall","Finset","Finset.instSetLike","Finset.le_sup'","Finset.mem_univ","Finset.sup'_le","Finset.univ","Finset.univ_nonempty","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianCoefficientSampleMesh_measurable","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.pow_const","MeasurableSpace","MeasureTheory.Integrable.mono'","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","Membership.mem","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NNReal","NPow.toPow","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMeasurableSpace","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","Norm.norm","NormedAddCommGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_normOneClass","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSemilatticeSup","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.norm","Real.norm_of_nonneg","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","le_of_not_gt","norm_nonneg","norm_pow","norm_sub_le","pow_le_pow_left\u2080","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralCoefficientMesh","name":"GinibrePoincare.brownianCoefficientSampleMesh_measurable","type_dependencies":["Fintype","GinibrePoincare.brownianCoefficientSampleMesh","Measurable","MeasurableSpace","NNReal","Nonempty","Real","Real.measurableSpace"],"value_dependencies":["BorelSpace.opensMeasurable","ContinuousSub.measurableSub\u2082","ContinuousSup.measurableSup\u2082","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Finset","Finset.instSetLike","Finset.sup'","Finset.sup'_apply","Finset.sup'_induction","Finset.univ","Finset.univ_nonempty","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","HEq","HEq.refl","HSub.hSub","HasSolidNorm.toTopologicalLattice","IsTopologicalAddGroup.to_continuousSub","Measurable","Measurable.norm","Measurable.sub","Measurable.sup","MeasurableSpace","Membership.mem","NNReal","Nonempty","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","Pi.instSemilatticeSup","Pi.instSub","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instMax","Real.instSemilatticeSup","Real.instSub","Real.lattice","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","TopologicalLattice.toContinuousSup","UniformSpace.toTopologicalSpace","eq_of_heq","funext","id","instHSub","instHasSolidNormReal","instIsTopologicalAddGroupReal","instSecondCountableTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralCoefficientMesh","name":"GinibrePoincare.brownianCoefficientSampleMesh_tendsto","type_dependencies":["ContinuousOn","Dist.dist","Filter","Filter.Tendsto","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","LE.le","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.pseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instPseudoMetricSpaceNNReal","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","And","And.casesOn","Classical.arbitrary","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ContinuousOn","Dist.dist","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Exists","Exists.casesOn","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.eventually","Filter.mp_mem","Filter.univ_mem'","Finset","Finset.instSetLike","Finset.le_sup'","Finset.mem_univ","Finset.sup'","Finset.sup'_lt_iff","Finset.univ","Finset.univ_nonempty","Fintype","GT.gt","GinibrePoincare.brownianCoefficientSampleMesh","HSub.hSub","Iff.mp","Iff.mpr","IsCompact.uniformContinuousOn_of_continuous","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Membership.mem","Metric.tendsto_nhds","Metric.uniformContinuousOn_iff","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instPreorder","Real.instSemilatticeSup","Real.instSub","Real.instZero","Real.linearOrder","Real.norm","Real.norm_of_nonneg","Real.normedCommRing","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","dist_eq_norm","dist_zero_right","gt_mem_nhds","id","instDistribLatticeOfLinearOrder","instHSub","instOrderTopologyReal","instPseudoMetricSpaceNNReal","nhds","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralCoefficientMesh","name":"GinibrePoincare.brownianCoefficientSampleMesh_tendsto_meanSquare","type_dependencies":["ContinuousOn","Dist.dist","Filter","Filter.Eventually","Filter.IsCountablyGenerated","Filter.Tendsto","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nonempty","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatNat","instPseudoMetricSpaceNNReal","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","BorelSpace.opensMeasurable","Classical.arbitrary","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousMul.measurableMul\u2082","ContinuousOn","Dist.dist","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Eventually.of_forall","Filter.IsCountablyGenerated","Filter.Tendsto","Filter.Tendsto.pow","Finset","Finset.instSetLike","Finset.le_sup'","Finset.mem_univ","Finset.sup'_le","Finset.univ","Finset.univ_nonempty","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianCoefficientSampleMesh_measurable","GinibrePoincare.brownianCoefficientSampleMesh_tendsto","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.pow_const","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_zero","MeasureTheory.tendsto_integral_filter_of_dominated_convergence","Membership.mem","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instCommSemiring","Nat.instMeasurableSpace","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_normOneClass","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","PartialOrder.toPreorder","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSemilatticeSup","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.norm","Real.norm_of_nonneg","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPseudoMetricSpaceNNReal","instSecondCountableTopologyReal","le_of_not_gt","nhds","norm_nonneg","norm_pow","norm_sub_le","not_false_eq_true","of_eq_true","pow_le_pow_left\u2080","rfl","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianPuncturedConcatenatedComparison","name":"GinibrePoincare.brownianConcatenated_initial_cutoff_difference","type_dependencies":["Eq","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.itoConcatenatedGrid","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianActualLeftGridSum_concatenated","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianInitialTimeCutoff_eq","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.itoConcatenatedGrid","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.coe_nonneg","NNReal.instSemiring","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring",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Ring","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.re","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.brownianConfigurationGrouping","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.configurationEuclideanEquiv_apply_zero","GinibrePoincare.ginibreConfigToEuclidean","InnerProductSpace.toNormedSpace","Nat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","congrArg","id","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalContinuousPathLaw","name":"GinibrePoincare.brownianConfigurationNoisePathMap","type_dependencies":["Fin","GinibrePoincare.Configuration","NNReal","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"],"value_dependencies":["Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.I","Complex.instAdd","Complex.instMul","Complex.instRCLike","Complex.ofReal","DivInvMonoid.toDiv","Field.toSemifield","Fin","Fin.instOfNat","GinibrePoincare.brownianConfigurationNoisePathMap._proof_1","GinibrePoincare.brownianConfigurationNoisePathMap._proof_2","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Prod","Prod.mk","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.normedField","Real.sqrt","Real.toNNReal","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalContinuousPathLaw","name":"GinibrePoincare.brownianConfigurationNoisePathMap._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalContinuousPathLaw","name":"GinibrePoincare.brownianConfigurationNoisePathMap._proof_2","type_dependencies":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalContinuousPathLaw","name":"GinibrePoincare.brownianConfigurationNoisePathMap_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.brownianConfigurationNoisePathMap","Measurable","MeasurableSpace.pi","NNReal","Nat","OfNat.ofNat","Prod","Real","Real.measurableSpace","instOfNatNat"],"value_dependencies":["Algebra.toSMul","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.I","Complex.addCommGroup","Complex.borelSpace","Complex.instAdd","Complex.instField","Comple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urable","CommRing.toRing","CommSemiring.toSemiring","Continuous","Continuous.continuousOn","ContinuousENorm.toENorm","ContinuousOn","Countable.LindelofSpace","Distrib.toAdd","Distrib.toMul","EDist","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Filter.atTop_neBot","Fintype","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.brownianUniformPartialSum_continuous","GinibrePoincare.brownianUniformPartialSum_martingale","GinibrePoincare.brownianUniformPartialSum_memLp_two","GinibrePoincare.brownianUniformPartialSum_tendsto_difference_meanSquare","GinibrePoincare.brownianUniformPartialSum_time_cap","GinibrePoincare.brownianUniformPartialSum_zero","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianFamilyPastSpace","GinibrePoincare.ginibreBrownianFamilyPastSpace_le","GinibrePoincare.realMartingale_terminal_cauchy_exists_continuous_martingale","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.mono","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.of_bound","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.aestronglyMeasurable_const","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.tendstoInMeasure_ae_unique","MeasureTheory.tendstoInMeasure_of_tendsto_ae","Membership.mem","MetricSpace.toEMetricSpace","Min.min","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","OrderTopology.of_linearLocallyFinite","PartialOrder.toPreorder","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal._auto_1","ProbabilityTheory.IsBrownianReal.cont","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun"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e.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","continuous_const","continuous_real_toNNReal","continuous_subtype_val","id","instHSub","instIsAddHaarMeasureVolume","instIsBotZeroClass","instIsTopologicalAddGroupReal","instOrderTopologyReal","instTopologicalSpaceSubtype","intervalIntegral","intervalIntegral.continuousOn_primitive_interval","isCompact_uIcc","zero_le"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralIntervalIsometry","name":"GinibrePoincare.brownianDisjointIntervalSum_isometry","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","DecidableEq","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommRing.toNonUnitalCommRing","ContinuousENorm.toENorm","DecidableEq","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownian_augmented_linear_disjoint_orthogonal","GinibrePoincare.ginibreBrownian_augmented_linear_memLp_two","GinibrePoincare.ginibreBrownian_augmented_linear_secondMoment","GinibrePoincare.ginibre_integral_square_sum_of_cross_zero","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LinearOrder.toDecidableEq","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.integral","MeasureTheory.integral_zero","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congrArg","congrFun'","dite","eq_self","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_comm","of_eq_true","rfl","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralIntervalIsometry","name":"GinibrePoincare.brownianDisjointIntervalSum_secondMoment_le","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","DecidableEq","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","DecidableEq","Distrib.toAdd","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.symm","Finset","Finset.instSetLike","Finset.sum","Finset.sum_le_sum","Finset.sum_mul","Finset.univ","Fintype","GinibrePoincare.brownianDisjointIntervalSum_isometry","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable_sq","MeasureTheory.integral","MeasureTheory.integral_mono","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","NNReal","NNReal.coe_nonneg","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instClosedIciTopology","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsOrderedModule","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTransEq_1","mul_le_mul_of_nonneg_left","norm_nonneg","pow_le_pow_left\u2080","sq_abs"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralIntervalConvergence","name":"GinibrePoincare.brownianDisjointSampleDifferences_tendsto_meanSquare","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ContinuousOn","DecidableEq","Dist.dist","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instPseudoMetricSpaceNNReal","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","ContinuousOn","ContinuousSub.measurableSub\u2082","Countable.LindelofSpace","DecidableEq","Dist.dist","Distrib.toAdd","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.mp","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Finset.le_sup'","Finset.mem_univ","Finset.sum","Finset.univ","Fintype","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianCoefficientSampleMesh_integrable_sq","GinibrePoincare.brownianCoefficientSampleMesh_tendsto_meanSquare","GinibrePoincare.brownianDisjointIntervalSum_secondMoment_le","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","Measurable","Measurable.mono","Measurable.sub","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.le","MeasureTheory.Filtration.mono","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.sub","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_nonneg","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow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Semiring","WithLp","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.ofLp","WithLp.toLp","Zero.toOfNat0","fact_one_le_two_ennreal","instDistribOfSemiring","instHAdd","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring.toSemiring","DFunLike.coe","DecidableEq","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.trans","EquivLike.toFunLike","EuclideanSpace","EuclideanSpace.inner_single_left","EuclideanSpace.single","Field.toSemifield","Finite.of_fintype","Finite.to_countable","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Fintype","Function.comp","GinibrePoincare.brownianFamily_augmented_orthogonal_fresh_increment","GinibrePoincare.brownianRadialFrame","GinibrePoincare.brownianRadialFrame_measurable","GinibrePoincare.brownianRadialFrame_radial_coordinate","GinibrePoincare.brownianRadialUnitVector","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.isotropicGaussian_coordinates_independent","GinibrePoincare.scaledStandardGaussian","HAdd.hAdd","HMul.hMul","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","Measurable","Measurable.comp","Measurable.prodMk","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MonoidHomClass.toOneHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonAssocSemiring.toMulZeroOneClass","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormOneClass.norm_one","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_normOneClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.module","PiLp","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.norm_single","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PiLp.seminormedAddCommGroup","PiLp.single","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.borelSpace","Real.instCompleteSpace","Real.instDivisionRing","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.ofLp","WithLp.toLp","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHAdd","instHMul","instHSub","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","map_one","measurable_fst","measurable_snd","of_eq_true","one_mul","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianAugmentedFreshIncrement","name":"GinibrePoincare.brownianFamily_fresh_increment_independent_augmented_variable","type_dependencies":["Distrib.toAdd","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HSub.hSub","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMea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normedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.ofLp","WithLp.toLp","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHAdd","instHMul","instHSub","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","map_one","measurable_fst","measurable_snd","of_eq_true","one_mul","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalContinuousPathLaw","name":"GinibrePoincare.brownianFamily_shift_continuous_noise_law_eq","type_dependencies":["Eq","Fin","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.brownianFamilyShift","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","NNReal","Nat","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Real","Real.measurableSpace","instOfNatNat"],"value_dependencies":["And.left","BorelSpace.mk","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CompactlyCoherentSpace.of_sequentialSpace","Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedField","Complex.instProperSpace","Complex.instT2Space","Complex.instZero","Complex.measurableSpace","Continuous","Continuous.measurable","ContinuousEvalConst.continuous_eval_const","ContinuousMap","ContinuousMap.compactConvergenceUniformSpace","ContinuousMap.compactOpen","ContinuousMap.instCompleteSpaceOfCompactlyCoherentSpace","ContinuousMap.instContinuousEvalConst","ContinuousMap.instFunLike","ContinuousMap.instIsCountablyGeneratedProdUniformityOfWeaklyLocallyCompactSpaceOfSigmaCompactSpace","ContinuousMap.instSeparableSpace","ContinuousMap.instT0Space","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Filter.Eventually.mono","Filter.EventuallyEq","Fin","Fin.fintype","FirstCountableTopology.frechetUrysohnSpace","FrechetUrysohnSpace.to_sequentialSpace","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.brownianConfigurationNoisePathMap","GinibrePoincare.brownianConfigurationNoisePathMap_measurable","GinibrePoincare.brownianFamilyShift","GinibrePoincare.brownianFamilyShift_isBrownian_independent","GinibrePoincare.brownianFamily_shift_whole_path_law_eq","GinibrePoincare.brownianScalar_whole_path_measurable","GinibrePoincare.continuousMap_law_eq_of_whole_path_law_eq","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianFullContinuousNoise_ae","GinibrePoincare.ginibreBrownianFullContinuousNoise_measurable","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.instBorelSpaceGinibreContinuousNoise","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","GinibrePoincare.instTopologicalSpaceGinibreContinuousNoise","IsClosed","IsClosed.isClosedEmbedding_subtypeVal","Measurable","Measurable.comp","MeasurableEmbedding.map_injective","MeasurableEmbedding.measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_congr","MeasureTheory.Measure.map_map","MeasureTheory.ae","MetricSpace.toEMetricSpace","NNReal","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","OfNat.ofNat","Pi.borelSpace","Pi.complete","Pi.instT0Space","Pi.instZero","Pi.t2Space","Pi.topologicalSpace","Pi.uniformSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set.ofPred","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","Topology.IsClosedEmbedding","Topology.IsClosedEmbedding.measurableEmbedding","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","congrArg","continuous_const","continuous_subt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AssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","ProbabilityTheory.HasGaussianLaw.memLp_two","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.covariance_eq_zero","ProbabilityTheory.IsGaussianProcess","ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_eval","ProbabilityTheory.IsGaussianProcess.indepFun_of_covariance_eq_zero","ProbabilityTheory.IsGaussianProcess.of_isGaussianProcess","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.covariance","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun.indepFun","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.injEq","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instCompleteSpace","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Iic","Set.instMembership","SetLike.instMembership","Singleton.singleton","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.mk","Subtype.val","Sum","Sum.casesOn","Sum.elim","Sum.inl","Sum.inr","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_eq_left._simp_1","congr","congrArg","continuous_apply","dite","eq_self","id","inferInstance","instDecidableEqProd","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","left_eq_add._simp_1","measurable_id","measurable_pi_apply","of_eq_true","or_true","rfl","true_and","true_or"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalPathLaw","name":"GinibrePoincare.brownianFamily_whole_path_law_eq","type_dependencies":["Eq","Fintype","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","NNReal","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Real","Real.measurableSpace"],"value_dependencies":["AEMeasurable","Eq","Eq.mpr","Eq.rec","Eq.refl","Fintype","GinibrePoincare.brownianScalar_whole_path_law_eq","GinibrePoincare.brownianScalar_whole_path_measurable","Measurable.aemeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","NNReal","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun.map_fun_eq_pi_map","Real","Real.measurableSpace","congrArg","funext","id"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplierMesh","type_dependencies":["HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instMulZeroClass","NeZero","Real","instHMul","instMulNat"],"value_dependencies":["Fin","Fin.fintype","Fin.val","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianFrozenMultiplierMesh._proof_1","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instDiv","Nat.instMulZeroClass","NeZero","Real","instHDiv","instHMul","instMulNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplierMesh._proof_1","type_dependencies":["Fin","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","Nonempty","instHMul","instMulNat"],"value_dependencies":["Fin","Fin.instInhabited","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","instHMul","instMulNat","instNonemptyOfInhabited"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplierMesh.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.brownianFrozenMultiplierMesh","HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instMulZeroClass","NeZero","Real","instHMul","instMulNat"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.brownianFrozenMultiplierMesh","HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instMulZeroClass","NeZero","Real","instHMul","instMulNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplierMesh.eq_1","type_dependencies":["Eq","Fin","Fin.fintype","Fin.val","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianFrozenMultiplierMesh","GinibrePoincare.brownianFrozenMultiplierMesh._proof_1","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instDiv","Nat.instMulZeroClass","NeZero","Real","instHDiv","instHMul","instMulNat"],"value_dependencies":["Eq.refl","GinibrePoincare.brownianFrozenMultiplierMesh","HMul.hMul","MulZeroClass.toZero","NNReal","Nat","Nat.instMulZeroClass","NeZero","Real","instHMul","instMulNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplierMesh_tendsto_meanSquare","type_dependencies":["ContinuousOn","Filter.Eventually","Filter.Tendsto","Filter.atTop","GinibrePoincare.brownianFrozenMultiplierMesh","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instNeZeroSucc","Nat.instPreorder","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instNeZeroNatHAdd_1","instNeZeroNatHMul","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Algebra.toModule","And","And.intro","And.left","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousOn","Countable.LindelofSpace","Dist.dist","Distrib.toAdd","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","Eq.mp","Eq.trans","Field.toSemifield","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Fin","Fin.fintype","Fin.instInhabited","Fin.is_lt","Fin.val","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.brownianCoefficientSampleMesh_tendsto_meanSquare","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coarse_dist_le_step","GinibrePoincare.itoUniformNNTime_common_samples_mem","GinibrePoincare.itoUniformNNTime_le_end","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","IsScalarTower.nnrat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.instOrderBot","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.cast_add","Nat.cast_one","Nat.instDiv","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul_pos","Nat.succ_pos","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrderTopology.of_linearLocallyFinite","PartialOrder.toPreorder","Preorder.toLE","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","bot_le","congr","congrArg","congrFun'","funext","instAddNat","instCommSemiringNNRat","instCountableNat","instDiscreteTopologyNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instIsCountablyGenerated_atTop","instIsTopologicalRingReal","instMulNat","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instNeZeroNatHMul","instNonemptyOfInhabited","instOfNatNat","instPseudoMetricSpaceNNReal","instTopologicalSpaceNat","mul_one_div","nhds","normedAlgebraRat","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","name":"GinibrePoincare.brownianFrozenMultiplier_difference_secondMoment_le","type_dependencies":["Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","Fintype","GinibrePoincare.brownianFrozenMultiplierMesh","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.instDiv","Nat.instMulZeroClass","Nat.mul_pos","Nat.ne_of_gt","NeZero.mk","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","BorelSpace.opensMeasurable","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMagma.toMul","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","ContinuousENorm.toENorm","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub\u2082","Decidable.decide","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","Fin.instLinearOrder","Fin.val","Finset","Finset.card","Finset.instSetLike","Finset.le_sup'","Finset.mem_univ","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.actualBoundedMultiplier_memLp_two","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianCoefficientSampleMesh_integrable_sq","GinibrePoincare.brownianDisjointIntervalSum_secondMoment_le","GinibrePoincare.brownianFrozenMultiplierMesh","GinibrePoincare.brownianFrozenMultiplierMesh._proof_1","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coarse_le_fine","GinibrePoincare.itoUniformNNTime_increment_sub_coe","GinibrePoincare.itoUniformNNTime_mono","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","LinearOrderedCommMonoidWithZero.toPosMulStrictMono","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Measurable","Measurable.aestronglyMeasurable","Measurable.mono","Measurable.mul","Measurable.sub","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.le","MeasureTheory.Filtration.mono","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.const_mul","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.of_bound","MeasureTheory.MemLp.sub","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_const_mul","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.addLeftMono","NNReal.instCommSemiring","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NNReal.instZero","NNReal.toReal","NPow.toPow","NSMul.toSMul","Nat","Nat.cast","Nat.cast_pos'","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instLinearOrderedCommMonoidWithZero","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.le_succ","Nat.mul_pos","Nat.ne_of_gt","Nat.succ_le_of_lt","Ne","NeZero.charZero_one","NeZero.mk","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Or.inl","Or.inr","PartialOrder","PartialOrder.toPreorder","Pi.instSub","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instDivInvMonoid","Re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"module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovPrefixLaw","name":"GinibrePoincare.brownianGirsanovCorrectedPrefix_eq","type_dependencies":["Eq","Finset.range","Finset.sum","GinibrePoincare.brownianGirsanovCorrectedPrefix","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","NNReal.instSub","NNReal.toReal","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Finset.range","Finset.sum","Finset.sum_range_sub","Finset.sum_sub_distrib","GinibrePoincare.brownianGirsanovCorrectedPrefix","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","NNReal.instSub","NNReal.toReal","Nat","OfNat.ofNat","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instSub","SubNegMonoid.toSub","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","congrArg","congrFun'","id","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovPrefixLaw","name":"GinibrePoincare.brownianGirsanovCorrectedPrefix_gaussian","type_dependencies":["ENNReal.ofReal","Finset.range","Finset.sum","Fintype","GinibrePoincare.brownianGirsanovCorrectedPrefix","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HSub.hSub","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.withDensity","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","Nat","Nat.instPreorder","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Real","Real.instZero","Real.measurableSpace","Semiring.toAddCommMonoid","Zero.toOfNat0","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.id","And","And.left","And.right","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousAdd.measurableMul\u2082","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","DFunLike.coe","Distrib.toAdd","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instOne","ENNReal.ofReal","Eq","Eq.mp","Eq.mpr","Eq.trans","Finset","Finset.instSetLike","Finset.measurable_sum","Finset.mem_range","Finset.range","Finset.sum","Finset.sum_range_succ","Fintype","Function.comp","Function.eval","GinibrePoincare.brownianGirsanovCorrectedPrefix","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.brownianPredictableVectorGaussianDensity_isProbabilityMeasure","GinibrePoincare.brownianPredictableVectorGaussianDensity_terminal_fresh_increment","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownian_augmented_coordinate_measurable_at","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mp","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.mono","Measurable.mul_const","Measurable.sub","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.mono","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsProbabilityMeasure.measure_univ","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.conv","MeasureTheory.Measure.dirac","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.Measure.map_const","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","MeasureTheory.MeasurePreserving.map_eq","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.measurePreserving_eval","Measure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type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","ENNReal.ofReal","Fin","Fin.val","Fintype","GinibrePoincare.brownianGirsanovCorrectedPrefix","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.withDensity","NNReal","NNReal.instDiv","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IdentDistrib","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Real","Real.instSub","Real.measurableSpace","Semiring.toNonAssocSemiring","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","ContinuousAdd.measurableMul\u2082","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal.ofReal","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.isLt","Fin.mk","Fin.sum_univ_eq_sum_range","Fin.val","Finset","Finset.instSetLike","Finset.measurable_sum","Finset.range","Finset.sum","Finset.sum_range_sub","Finset.univ","Fintype","GinibrePoincare.brownianGirsanovCorrectedPrefix","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.brownianPredictableVectorGaussianDensity_corrected_grid_identDistrib","GinibrePoincare.brownianUniformNNTime_rational_endpoint","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_mono","GinibrePoincare.itoUniformTime","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Measurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.withDensity","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instDiv","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.cast_zero","Nat.instPreorder","Nat.le_of_lt_succ","Nat.mul_le_mul_right","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IdentDistrib","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instMul","Real.instNatCast","Real.instRing","Real.instSub","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_zero","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","funext","id","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instIsTopologicalRingReal","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instSecondCountableTopologyReal","lt_of_lt_of_le","measurable_pi_apply","measurable_pi_lambda","of_eq_true","zero_div"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder","type_dependencies":["InnerProductSpace","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","Semiring.toNonAssocSemiring"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","GinibrePoincare.brownianHouseholder._proof_1","GinibrePoincare.brownianHouseholder._proof_2","GinibrePoincare.brownianHouseholder._proof_3","GinibrePoincare.brownianHouseholder._proof_4","InnerProductSpace","InnerProductSpace.toNormedSpace","LinearIsometryEquiv.neg","LinearIsometryEquiv.trans","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring","Set","Set.instSingletonSet","Singleton.singleton","Submodule.reflection","Submodule.span"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder._proof_1","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHom.id","RingHomInvPair","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHomInvPair.ids","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder._proof_2","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder._proof_3","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","Real.semiring","Set","Set.instSingletonSet","Singleton.singleton","Submodule.HasOrthogonalProjection","Submodule.span"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","FiniteDimensional.RCLike.properSpace_submodule","FiniteDimensional.span_singleton","InnerProductSpace","InnerProductSpace.toNormedSpace","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","RCLike.toDenselyNormedField","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","Real.semiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instSingletonSet","SetLike.instMembership","Singleton.singleton","Submodule","Submodule.HasOrthogonalProjection.ofCompleteSpace","Submodule.setLike","Submodule.span","Subtype","Subtype.pseudoMetricSpace","complete_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalHouseholder","name":"GinibrePoincare.brownianHouseholder_apply","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Eq","EquivLike.toFunLike","GinibrePoincare.brownianHouseholder","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGro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","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralInitialCutoff","name":"GinibrePoincare.brownianInitialTimeCutoff_bound","type_dependencies":["GinibrePoincare.brownianInitialTimeCutoff","LE.le","NNReal","Norm.norm","Real","Real.instLE","Real.norm"],"value_dependencies":["DivInvMonoid.toDiv","Eq","Eq.mpr","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianInitialTimeCutoff.eq_1","HDiv.hDiv","HMul.hMul","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","LE.le","LE.le.trans","MulZeroOneClass.toMulOneClass","NNReal","NNReal.toReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Real.smoothTransition","Real.smoothTransition.le_one","Real.smoothTransition.nonneg","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","abs","abs_of_nonneg","congrArg","congrFun'","id","instHDiv","instHMul","instHSub","instMulZeroOneClassOfSemiring","mul_le_mul_of_nonneg_right","norm_mul","norm_nonneg","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralInitialCutoff","name":"GinibrePoincare.brownianInitialTimeCutoff_continuous","type_dependencies":["Continuous","ContinuousOn","GinibrePoincare.brownianInitialTimeCutoff","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instZero","Real.pseudoMetricSpace","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous","Continuous.continuousAt","ContinuousAt","ContinuousAt.comp","ContinuousAt.congr","ContinuousAt.div_const","ContinuousAt.mul","ContinuousOn","ContinuousOn.continuousAt","DistribLattice.toLattice","DivInvMonoid.toDiv","Eq","Eq.ndrec","Eq.symm","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.Tendsto.eventually","Filter.Tendsto.sub_const","Filter.mp_mem","Filter.univ_mem'","Function.comp","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianInitialTimeCutoff_zero","HDiv.hDiv","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mpr","IsOpen.mem_nhds","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder.toDecidableEq","Membership.mem","NNReal","NNReal.continuous_coe","NNReal.instLinearOrder","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Ne.symm","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Not","OfNat.ofNat","One.toOfNat1","OrderTopology.to_orderClosedTopology","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddGroup","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMul","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.smoothTransition","Real.smoothTransition.continuous","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","Set","Set.Ioi","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","bot_le","continuousAt_const","continuous_iff_continuousAt","dite","eventually_lt_nhds","id","instClosedIciTopology","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHDiv","instHSub","instHasSolidNormReal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","isOpen_Ioi","lt_of_le_of_ne","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralInitialCutoff","name":"GinibrePoincare.brownianInitialTimeCutoff_difference_bound","type_dependencies":["GinibrePoincare.brownianInitialTimeCutoff","HSub.hSub","LE.le","NNReal","Norm.norm","Real","Real.instLE","Real.instSub","Real.norm","instHSub"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne.toAddGroupWithOne","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toOne","AddSemigroup.toAdd","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianInitialTimeCutoff.eq_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","Mul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocCommRing.toNonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Real.smoothTransition","Real.smoothTransition.le_one","Real.smoothTransition.nonneg","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","le_of_not_gt","mul_le_mul_of_nonneg_right","norm_mul","norm_nonneg","one_mul","one_sub_mul","rfl","sub_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralInitialCutoff","name":"GinibrePoincare.brownianInitialTimeCutoff_eq","type_dependencies":["Eq","GinibrePoincare.brownianInitialTimeCutoff","HMul.hMul","LE.le","LT.lt","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instZero","Zero.toOfNat0","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"v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ianIntegralGirsanovVectorFinite","name":"GinibrePoincare.brownianPredictableVectorGaussianDensity_succ","type_dependencies":["Eq","Fintype","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.gaussianVectorExponentialTilt","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","NNReal.instSub","Nat","OfNat.ofNat","Real","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","DivInvMonoid.toDiv","Eq","Eq.trans","Finset.range","Finset.sum","Finset.sum_range_succ","Finset.univ","Fintype","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.brownianPredictableVectorGaussianDensity._proof_1","GinibrePoincare.gaussianVectorExponentialTilt","GinibrePoincare.gaussianVectorExponentialTilt_eq_exp","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NNReal.instSub","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.exp","Real.exp_add","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","True","congr","congrArg","eq_self","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovTerminalFresh","name":"GinibrePoincare.brownianPredictableVectorGaussianDensity_terminal_fresh_increment","type_dependencies":["And","ENNReal.ofReal","Fintype","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instSub","NNReal.toReal","Nat","Nat.instPreorder","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Real","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dependencies":["And","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","ENNReal.ofReal","Eq","Eq.mpr","Eq.trans","Fintype","Function.comp","GinibrePoincare.brownianPredictableVectorGaussianDensity","GinibrePoincare.brownianPredictableVectorGaussianDensity_fresh_increment","GinibrePoincare.brownianPredictableVectorGaussianDensity_isProbabilityMeasure","GinibrePoincare.brownianPredictableVectorGaussianDensity_past_map","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownian_augmented_coordinate_measurable_at","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.mono","Measurable.mul_const","Measurable.prodMk","Measurable.sub","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.le","MeasureTheory.Filtration.mono","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.prod","MeasureTheory.Measure.withDensity","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instSub","NNReal.toReal","Nat","Nat.instPreorder","Nat.le_succ","Nat.succ","Nat.succ_le_of_lt","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","PartialOrder.toPreorder","Pi.instSub","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.map_prod_eq_prod_map_map","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.indepFun_iff_map_prod_eq_prod_map_map","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddGroup","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr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ike"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRadialDirection","name":"GinibrePoincare.brownianRadialUnitVector_continuousAt","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CompleteSpace","ContinuousAt","GinibrePoincare.brownianRadialUnitVector","InnerProductSpace","Ne","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Classical.propDecidable","Compl.compl","CompleteSpace","Continuous.continuousAt","ContinuousAt.congr","ContinuousAt.inv\u2080","ContinuousAt.smul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","Eq","Eq.mp","Eq.trans","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.brownianRadialUnitVector","HSMul.hSMul","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsOpen.mem_nhds","IsTopologicalDivisionRing.toContinuousInv\u2080","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Ne","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedSpace.toModule","Not","OfNat.ofNat","Pi.instInv","Pi.smul'","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","Set","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.ofPred","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T5Space.toT1Space","T6Space.toT5Space","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreStochasticRadialDirection.0.GinibrePoincare.brownianRadialUnitVector_continuousAt._simp_1_1","_private.GinibrePoincare.Analysis.GinibreStochasticRadialDirection.0.GinibrePoincare.brownianRadialUnitVector_continuousAt._simp_1_2","congrArg","congrFun'","continuousAt_id","continuous_norm","eq_false","eq_self","id","instHSMul","instIsTopologicalDivisionRingReal","instPolynormableSpace","instT6SpaceOfMetrizableSpace","isOpen_compl_singleton","ite_eq_right_of_eq_false","nhds","norm_ne_zero_iff","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalRadialFrame","name":"GinibrePoincare.brownianRadialUnitVector_measurable","type_dependencies":["BorelSpace","CompleteSpace","GinibrePoincare.brownianRadialUnitVector","InnerProductSpace","Measurable","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SecondCountableTopology","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","BorelSpace.opensMeasurable","Classical.propDecidable","CompleteSpace","ContinuousInv\u2080.measurableInv","ContinuousSMul.measurableSMul\u2082","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Eq","Field.toSemifield","GinibrePoincare.brownianRadialUnitVector","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsTopologicalDivisionRing.toContinuousInv\u2080","Measurable","Measurable.fun_inv","Measurable.fun_smul","Measurable.ite","Measurable.norm","MeasurableSingletonClass.measurableSet_singleton","MeasurableSpace","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpac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al.instOne","Real.instRing","Real.linearOrder","Real.partialOrder","Real.semiring","instHAdd","instHDiv","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.brownianRationalApproxIndex","NNReal","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovContinuousTime","name":"GinibrePoincare.brownianRationalApproxIndex_le","type_dependencies":["GinibrePoincare.brownianRationalApproxIndex","HAdd.hAdd","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","CommSemiring.toSemiring","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","GinibrePoincare.brownianRationalApproxIndex","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","Nat.ble","Nat.cast","Nat.cast_add","Nat.cast_nonneg'","Nat.cast_one","Nat.floor","Nat.floor_mono","Nat.floor_natCast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","div_le_one","id","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instLENat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","le_of_lt","mul_le_mul_of_nonneg_right","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovContinuousTime","name":"GinibrePoincare.brownianRationalApproxTime_tendsto","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Filter.Tendsto","Filter.atTop","GinibrePoincare.brownianRationalApproxIndex","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LT.lt","NNReal","NNReal.instDiv","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.cast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Semiring.toNonAssocSemiring","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instOfNatNat","nhds"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Decidable.decide","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.const_mul","Filter.atTop","Filter.tendsto_atTop_add_const_right","FloorRing.toFloorSemiring","Function.comp","GinibrePoincare.brownianRationalApproxIndex","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopological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qFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_sub","MeasureTheory.Lp.instDist","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instLattice","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instSub","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instPreorder","Prod.snd","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.lattice","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.sqrt","Real.sqrt_sq_eq_abs","Real.sqrt_zero","SemilatticeSup.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","cauchySeq_iff_tendsto_dist_atTop_0","congrArg","congrFun'","dist_eq_norm","fact_one_le_two_ennreal","funext","id","instAddNat","instHAdd","instHPow","instHSub","instInhabitedNat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","nhds","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianConcatenatedComparison","name":"GinibrePoincare.brownianUniformLeftSum_concatenated_difference_tendsto_meanSquare","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ContinuousOn","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fintype","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoConcatenatedGrid","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instHAdd","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast",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wnianUniformLeftSum_concatenated_difference_tendsto_meanSquare._proof_1_2","congr","congrArg","congrFun'","eq_self","funext","instAddNat","instCommSemiringNNRat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_one_div","nhds","normedAlgebraRat","of_eq_true","tendsto_one_div_add_atTop_nhds_zero_nat","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianPuncturedConcatenatedComparison","name":"GinibrePoincare.brownianUniformLeftSum_concatenated_punctured_difference_tendsto_meanSquare","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ContinuousOn","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fintype","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoConcatenatedGrid","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instHAdd","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toModule","Algebra.to_smulCommClass","Bool","Bool.false","Bool.true","BorelSpace.opensMeasurable","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Continuous.continuousOn","ContinuousENorm.toENorm","ContinuousOn","Decidable.decide","Distrib.toAdd","Distrib.toMul","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.const_add","Filter.Tendsto.const_mul","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","Finset.sum_const_zero","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.actualMeanSquare_difference_le_four_errors","GinibrePoincare.brownianActualLeftGridSum","GinibrePoincare.brownianActualLeftGridSum_concatenated","GinibrePoincare.brownianActualLeftGridSum_memLp_two","GinibrePoincare.brownianConcatenated_initial_cutoff_difference","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianInitialTimeCutoff_adapted","GinibrePoincare.brownianInitialTimeCutoff_bound","GinibrePoincare.brownianInitialTimeCutoff_continuous","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.brownianUniformLeftSum_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inormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","ContinuousOn","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.mp","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Fintype","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.brownianUniformLeftSum_difference_secondMoment_le_mesh","GinibrePoincare.brownianUniformRefinementMesh","GinibrePoincare.brownianUniformRefinementMesh_tendsto_meanSquare","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Measurable","Measurable.mono","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_nonneg","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instPreorder","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.Icc","Set.instMembership","StarOrderedRing.toExistsAddOfLE","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","instAddNat","instClosedIciTopology","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsOrderedModule","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","le_rfl","nhds","sq_nonneg","squeeze_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovRationalGrid","name":"GinibrePoincare.brownianUniformNNTime_rational_endpoint","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","HMul.hMul","LT.lt","NNReal","NNReal.instDiv","NNReal.instSemiring","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Decidable.decide","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coe","GinibrePoincare.itoUniformTime","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","LT.lt","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.coe_injective","NNReal.coe_natCast","NNReal.instDiv","NNReal.instSemiring","NNReal.toReal","Nat","Nat.cast","Nat.cast_mul","Nat.cast_ne_zero","Nat.ne_of_gt","Ne","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.mk","Prod.snd","Real","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMul","Real.instNatCast","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semiring.toNonAssocSemiring","True","Zero.toOfNat0","congr","congrArg","congr_arg\u2082","div_one","eq_self","id","inferInstance","instDistribOfSemiring","instHDiv","instHMul","instIsCancelMulZero","instLTNat","instMulNat","instOfNat","instOfNatNat","mul_one","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGirsanovRationalGrid","name":"GinibrePoincare.brownianUniformNNTime_rational_prefix","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","HMul.hMul","LT.lt","NNReal","NNReal.instDiv","NNReal.instSemiring","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Decidable.decide","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coe","GinibrePoincare.itoUniformTime","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","LT.lt","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq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rePoincare.Analysis.FiniteDimensionalItoWeightedRefinement.0.GinibrePoincare.brownianUniformPartialSum_grid_endpoint._proof_1_3","add_zero","congrArg","congrFun'","eq_self","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","instSubNat","max_eq_left","max_eq_right","min_eq_left","min_eq_right","of_eq_true","rfl","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoWeightedRefinement","name":"GinibrePoincare.brownianUniformPartialSum_grid_increment","type_dependencies":["Eq","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","NNReal","Nat","OfNat.ofNat","Real","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toRing","CommSemiring.toSemiring","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Finset.range","Finset.sum","Finset.sum_range_succ","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.brownianUniformPartialSum_grid_endpoint","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","LT.lt.le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NNReal","NPow.toPow","Nat","Nat.decLe","Nat.instCommSemiring","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instSub","Ring","Ring.toAddCommGroup","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","_private.GinibrePoincare.Analysis.FiniteDimensionalItoWeightedRefinement.0.GinibrePoincare.brownianUniformPartialSum_grid_increment._proof_1_1","congrArg","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralHorizonComparison","name":"GinibrePoincare.brownianUniformPartialSum_horizon_difference_tendsto_meanSquare","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ContinuousOn","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fintype","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreB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iring","NNReal.instLinearOrder","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instOrderBot","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_add","Nat.cast_nonneg'","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Nat.succ_pos","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Or.inl","Or.inr","Or.resolve_left","Or.resolve_right","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.ext","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioc","Set.Ioc_disjoint_Ioc","Set.instCompleteAtomicBooleanAlgebra","Set.instMembership","Set.mem_Icc._simp_1","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreBrownianIntegralHorizonComparison.0.GinibrePoincare.brownianUniformPartialSum_horizon_difference_tendsto_meanSquare._simp_1_1","add_nonneg","add_tsub_cancel_of_le","add_zero","and_self","bot_le","congr","congrArg","congrFun","congrFun'","dist_self","dite","div_eq_mul_inv","eq_of_heq","eq_self","funext","id","if_neg","if_pos","instAddNat","instCommSemiringNNRat","instDecidableEqFin","instDecidableEqProd","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instNonemptyOfInhabited","instNonemptyProd","instOfNatAtLeastTwo","instOfNatNat","instPseudoMetricSpaceNNReal","instReflLe","instStarRingNNReal","ite","ite_congr","ite_eq_left_of_eq_true","le_max_left","le_total","max_eq_left","max_eq_right","min_le_iff","nhds","normedAlgebraRat","not_le","of_eq_true","one_mul","pos_iff_ne_zero","rfl","sub_self","tendsto_one_div_add_atTop_nhds_zero_nat","tsub_pos_iff_lt","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedPartialBound","name":"GinibrePoincare.brownianUniformPartialSum_initial_cutoff_error_bound","type_dependencies":["DivInvMonoid.toDiv","Fintype","GinibrePoincare.brownianInitialTimeCutoff","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNRe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ormedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","EmptyCollection.emptyCollection","Eq","Eq.mpr","Eq.trans","Finset","Finset.induction_on","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_apply","Finset.sum_insert","Fintype","GinibrePoincare.brownianFrozenStep","GinibrePoincare.brownianFrozenStep_martingale","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_mono","HAdd.hAdd","InnerProductSpace.toNormedSpace","Insert.insert","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Martingale.add","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.martingale_zero","Membership.mem","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.le_succ","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommMonoid","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","congrArg","congrFun","eq_self","funext","id","instAddNat","instDecidableEqNat","instHAdd","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralPartialCauchy","name":"GinibrePoincare.brownianUniformPartialSum_memLp_two","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fintype","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toNonUnitalCommRing","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENorm","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toContinuousENorm","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Finset","Finset.instSetLike","Finset.range","Finset.sum","Fintype","GinibrePoincare.brownianFrozenStep","GinibrePoincare.brownianFrozenStep_memLp_two","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HEq","HEq.refl","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.memLp_finsetSum","Membership.mem","NNReal","NNReal.instPart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ibrePoincare.brownianUniformPartialSum_zero","type_dependencies":["Eq","GinibrePoincare.brownianUniformPartialSum","NNReal","NNReal.instZero","Nat","OfNat.ofNat","Real","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","Finset.range","Finset.sum","Finset.sum_const_zero","GinibrePoincare.brownianFrozenStep","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Max.max","Min.min","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","NNReal.instZero","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instMul","Real.instSub","Real.instZero","Real.semiring","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SubNegMonoid.toAddMonoid","True","Zero.toOfNat0","congrArg","congrFun'","eq_self","funext","inf_of_le_left","instAddNat","instHAdd","instHMul","instHSub","instMulZeroClassOfSemiring","instOfNatNat","of_eq_true","sub_self","sup_of_le_left","zero_le._simp_1"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralRefinementBound","name":"GinibrePoincare.brownianUniformRefinementMesh","type_dependencies":["NNReal","Nat","Real"],"value_dependencies":["Fin","Fin.fintype","Fin.val","GinibrePoincare.brownianCoefficientSampleMesh","GinibrePoincare.brownianUniformRefinementMesh._proof_1","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","NNReal","Nat","Nat.instDiv","OfNat.ofNat","Real","instAddNat","instHAdd","instHDiv","instHMul","instMulNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralRefinementBound","name":"GinibrePoincare.brownianUniformRefinementMesh._proof_1","type_dependencies":["Fin","HAdd.hAdd","HMul.hMul","Nat","Nonempty","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dependencies":["Fin","Fin.instInhabited","HAdd.hAdd","HMul.hMul","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instNeZeroNatHAdd_1","instNeZeroNatHMul","instNonemptyOfInhabited","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralMeanSquareCauchy","name":"GinibrePoincare.brownianUniformRefinementMesh_tendsto_meanSquare","type_dependencies":["ContinuousOn","Filter.Eventually","Filter.Tendsto","Filter.atTop","GinibrePoincare.brownianUniformRefinementMesh","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instPreorder","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.fst","Prod.instPreorder","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Algebra.toModule","And","And.left","And.right","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousOn","Countable.LindelofSpace","Dist.dist","Distrib.toAdd","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.trans","Field.toSemifield","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.comp","Filter.Tendsto.const_mul","Filter.atTop","Filter.instIsCountablyGeneratedAtTopProd","Filter.instSProd","Filter.tendsto_fst","Filter.tendsto_snd","Fin","Fin.fintype","Fin.instInhabited","Fin.is_lt","Fin.val","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.brownianCoefficientSampleMesh_tendsto_meanSquare","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_common_samples_mem","GinibrePoincare.itoUniformNNTime_two_coarse_dist_le","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","IsScalarTower.nnrat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.cast_add","Nat.cast_one","Nat.instDiv","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instNeZeroSucc","Nat.instPreorder","Nat.succ_pos","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrderTopology.of_linearLocallyFinite","PartialOrder.toPreorder","Prod","Prod.fst","Prod.instPreorder","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SProd.sprod","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreBrownianIntegralMeanSquareCauchy.0.GinibrePoincare.brownianUniformRefinementMesh_tendsto_meanSquare._simp_1_1","congr","congrArg","congrFun'","funext","id","instAddNat","instCommSemiringNNRat","instCountableNat","instDiscreteTopologyNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instIsCountablyGenerated_atTop","instIsTopologicalRingReal","instMulNat","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instNeZeroNatHMul","instNonemptyOfInhabited","instOfNatNat","instPseudoMetricSpaceNNReal","instTopologicalSpaceNat","mul_one_div","nhds","normedAlgebraRat","tendsto_one_div_add_atTop_nhds_zero_nat","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianBrownian","name":"GinibrePoincare.brownianUnitField_actual_integral_isBrownian","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Continuous","DecidableEq","Distrib.toAdd","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Filter.Eventually","Filter.EventuallyEq","Filter.atTop","Fintype","GinibrePoincare.brownianUnitShiftedUniformSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","HSub.hSub","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.StronglyAdapted","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instPreorder","Norm.norm","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp.innerProductSpace._proof_1","PiLp.instNorm","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.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itoUniformNNTime","GinibrePoincare.itoUniformNNTime_mono","HAdd.hAdd","HMul.hMul","HSub.hSub","Inner.inner","InnerProductSpace.toInner","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toIsOrderedAddMonoid","Membership.mem","Monotone","Monotone.add","NNReal","NNReal.addLeftMono","NNReal.instIsOrderedRing_1","NNReal.instPartialOrder","NNReal.instSemiring","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PartialOrder.toPreorder","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","WithLp.ofLp","WithLp.toLp","congr","congrArg","congrFun'","conj_trivial","eq_self","fact_one_le_two_ennreal","funext","id","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","instTrivialStarReal","monotone_const","mul_comm","of_eq_true","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianShifted","name":"GinibrePoincare.brownianUnitShiftedUniformSum_gaussian_independent","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","DecidableEq","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fintype","GinibrePoincare.brownianUnitShiftedUniformSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","NNReal.instPartialOrder","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp.innerProductSpace._proof_1","PiLp.instNorm","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Real","Real.instOne","Real.instZero","Real.measurableSpace","Real.norm","WithLp.measurableSpace","Zero.toOfNat0","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","CharP.cast_eq_zero","CharP.ofCharZero","DecidableEq","Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","EuclideanSpace","Field.toSemifield","Finset.range","Finset.sum","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.brownianUnitGridPrefix","GinibrePoincare.brownianUnitGridPrefix_gaussian","GinibrePoincare.brownianUnitGridPrefix_independent_past","GinibrePoincare.brownianUnitShiftedUniformSum","GinibrePoincare.brownianUnitShiftedUniformSum_eq_prefix","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_end","GinibrePoincare.itoUniformNNTime_mono","GinibrePoincare.monotoneGrid_duration_sum_from_start","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toIsOrderedAddMonoid","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MonoidWithZero.toMulZeroOneClass","Monotone","Monotone.add","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.addLeftMono","NNReal.addLeftReflectLT","NNReal.instAddCancelCommMonoid","NNReal.instIsOrderedRing_1","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp.innerProductSpace._proof_1","PiLp.instNorm","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun._auto_1","ProbabilityTheory.IsPreBrownianRe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.StrongConvexQuantileTransport","name":"GinibrePoincare.cdfQuantileTransport.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.cdfQuantileTransport","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioi","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.cdfQuantileTransport","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioi","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileTransport","name":"GinibrePoincare.cdfQuantileTransport_derivative_bound","type_dependencies":["And","Eq","GinibrePoincare.cdfQuantileTransport","GinibrePoincare.densityQuantileProfile","HMul.hMul","Inv.inv","LE.le","LT.lt","Membership.mem","OfNat.ofNat","One.toOfNat1","Real","Real.instInv","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioi","Set.Ioo","Set.image","Set.instMembership","Set.univ","StrictMono","StrictMono.strictMonoOn","StrictMonoOn","Zero.toOfNat0","instHMul"],"value_dependencies":["And","And.intro","CommGroupWithZero.toGroupWithZero","CommMagma.toMul","CommRing.toNonUnitalCommRing","Decidable","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.cdfQuantileTransport","GinibrePoincare.densityQuantileProfile","GinibrePoincare.increasingCDFQuantileOn","GinibrePoincare.increasingCDFQuantileOn_mem","GinibrePoincare.increasingCDFQuantileOn_right_inverse","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","Iff.mpr","Inv.inv","InvOneClass.toInv","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Real","Real.commRing","Real.decidableLT","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Set","Set.Ioi","Set.Ioo","Set.decidableMemIoo","Set.image","Set.instMembership","Set.mem_image_of_mem","Set.mem_univ","Set.univ","StrictMono","StrictMono.injective","StrictMono.strictMonoOn","StrictMonoOn","Zero.toOfNat0","congr","congrArg","div_eq_mul_inv","div_le_div_iff\u2080","id","if_pos","instHDiv","instHMul","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","inv_eq_one_div","inv_nonneg","ite","ite_congr","mul_comm","mul_nonneg","mul_one"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileTransport","name":"GinibrePoincare.cdfQuantileTransport_hasDerivAt","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","GinibrePoincare.cdfQuantileTransport","HMul.hMul","HasDerivAt","InnerProductSpace.toNormedSpace","Inv.inv","Membership.mem","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instInv","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Ioi","Set.Ioo","Set.image","Set.instMembership","Set.univ","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instPolynormableSpace"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Eq","Eq.rec","Field.toSemifield","GinibrePoincare.increasingCDFQuantileOn","GinibrePoincare.increasingCDFQuantileOn_hasDerivAt","HasDerivAt","HasDerivAt.comp","InnerProductSpace.toNormedSpace","Inv.inv","Membership.mem","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instInv","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Ioi","Set.Ioo","Set.image","Set.instMembership","Set.mem_image_of_mem","Set.mem_univ","Set.ordConnected_Ioi","Set.univ","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexTransportMeasure","name":"GinibrePoincare.cdfQuantileTransport_map","type_dependencies":["Eq","GinibrePoincare.cdfQuantileTransport","LE.le","Measurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.cdf","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.pseudoMetricSpace","Set","Set.Ioi","Set.Ioo","Set.image","Set.univ","StieltjesFunction.toFun","StrictMono","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["BorelSpace.opensMeasurable","DFunLike.coe","Decidable.byContradiction","DistribLattice.toLattice","ENNReal","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_zero","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.cdfQuantileTransport","GinibrePoincare.increasingCDFQuantileOn","GinibrePoincare.increasingCDFQuantileOn_mem","GinibrePoincare.increasingCDFQuantileOn_right_inverse","HasSolidNorm.orderClosedTopology","Iff","Iff.intro","Iff.mp","Iff.mpr","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Measurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.ext_of_Iic","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.measure_empty","Membership.mem","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","ProbabilityTheory.cdf","ProbabilityTheory.ofReal_cdf","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.decidableLE","Real.decidableLT","Real.instIsOrderedAddMonoid","Real.instLE","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","Set","Set.Iic","Set.Ioi","Set.Ioo","Set.eq_empty_iff_forall_notMem","Set.ext","Set.image","Set.instEmptyCollection","Set.instMembership","Set.mem_image_of_mem","Set.mem_univ","Set.preimage","Set.univ","StieltjesFunction.toFun","StrictMono","StrictMono.le_iff_le","StrictMono.monotone","StrictMono.strictMonoOn","StrictMonoOn","StrictMonoOn.monotoneOn","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","dite","eq_self","id","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHasSolidNormReal","instOrderTopologyReal","instSecondCountableTopologyReal","le_of_not_gt","lt_of_le_of_lt","lt_of_not_ge","measurableSet_Iic","not_le_of_gt","not_lt_of_ge","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexCDF","name":"GinibrePoincare.cdf_withDensity_eq_densityCDF","type_dependencies":["ENNReal.ofReal","Eq","GinibrePoincare.densityCDF","LE.le","Measurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","OfNat.ofNat","ProbabilityTheory.cdf","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.pseudoMetricSpace","StieltjesFunction.toFun","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["BorelSpace.opensMeasurable","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.ofReal","ENNReal.toReal","Eq","Eq.mpr","Eq.symm","Filter.Eventually.of_forall","GinibrePoincare.densityCDF","HasSolidNorm.orderClosedTopology","LE.le","Measurable","Measurable.aestronglyMeasurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.real","MeasureTheory.Measure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ormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instPow","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.ext","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","Set.univ","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","Trans.trans","True","True.intro","UniformSpace.toTopologicalSpace","WithLp","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","WithLp.toLp","WithTop.some","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_false","eq_self","eq_true","fact_one_le_two_ennreal","fderiv","funext","id","instContinuousSMulForall","instDecidableEqFin","instFintypeProd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSecondCountableTopologyReal","instTopENat","instTransEq","inv_mul_cancel\u2080","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","not_false","not_false_eq_true","of_eq_true","one_div","one_mul","secondCountableTopologyEither_of_right","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionEquality","name":"GinibrePoincare.centerOfMassReal_complex_decomposition","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instOne","Complex.instStarRing","Complex.ofReal","DFunLike.coe","DivInvMonoid.toDiv","Eq","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.coordinateSum","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHAdd","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.ext","Complex.im","Complex.instAdd","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.inv_im","Complex.inv_re","Complex.mul_im","Complex.mul_re","Complex.normSq","Complex.normSq_ofNat","Complex.ofReal","Complex.re","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.coordinateSum","GroupWithZero.toDivisionMonoid","GroupWithZero.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iv","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","iteratedDeriv","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","mul_one","neg_eq_zero","rfl","sq_abs","sq_nonneg","sub_add_cancel","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.TaylorDifferenceQuotient","name":"GinibrePoincare.centeredDifference_square_error_bound","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.centeredDifference","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.lattice","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","abs","deriv","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","iteratedDeriv"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.centeredDifference","GinibrePoincare.centeredDifference_error_bound","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.ad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roup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.measurableSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GaussianFourierUniqueness.0.GinibrePoincare.integrable_max_zero","aestronglyMeasurable_id","congrArg","congrFun'","continuous_id'","eq_self","fact_one_le_two_ennreal","id","instCountableFin","instCountableProd","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsBotZeroClass","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","integral_withDensity_eq_integral_toReal_smul\u2080","of_eq_true","sup_of_le_left","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.charFun_euclideanImagParts_eq_of_fourierTest_eq_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.euclideanImagPartNegativeMeasure","GinibrePoincare.euclideanImagPartPositiveMeasure","GinibrePoincare.gaussianL2FourierTest","InnerProductSpace.toInner","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.charFun","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_sub._simp_1","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","DFunLike.coe","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.charFun_euclideanImagPartNegativeMeasure","GinibrePoincare.charFun_euclideanImagPartPositiveMeasure","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.euclideanImagPartNegativeMeasure","GinibrePoincare.euclideanImagPartPositiveMeasure","GinibrePoincare.gaussianL2FourierTest","GinibrePoincare.integrable_im_Lp_two","GinibrePoincare.integral_im_mul_configurationFourierCharacter_eq_zero","HEq","HEq.refl","HMul.hMul","HSub.hSub","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","Lattice.toSemilatticeSup","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Integrable.neg","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.charFun","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_sub","Membership.mem","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.to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ialGenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialGeneratorGraph","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.continuousAdd","Prod.continuousConstSMul","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.topologicalClosure","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialGenerator._proof_1","GinibrePoincare.closedPolynomialGenerator._proof_2","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialGeneratorGraph","GinibrePoincare.polynomialGeneratorGraph._proof_1","GinibrePoincare.polynomialGeneratorGraph._proof_2","GinibrePoincare.polynomialGeneratorGraph._proof_4","GinibrePoincare.polynomialGeneratorGraph._proof_5","GinibrePoincare.polynomialGeneratorGraph_closure_singleValued","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule.toLinearPMap_graph_eq","Submodule.topologicalClosure","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorWeakCore","name":"GinibrePoincare.closedPolynomialGenerator_graph_le_weakCoreGraph","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakCoreGraph","GinibrePoincare.polynomialEigenfunction_full_core_weak_equation._proof_2","InnerProductSpace.toNormedSpace","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.instPartialOrder","Subtype","UniformSpace.toTopologicalSpace","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Decidable.byContradiction","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Exists.casesOn","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.closedPolynomialGenerator_eigenvalue","GinibrePoincare.closedPolynomialGenerator_graph","GinibrePoincare.coreObservableL2","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregeneratorL2","GinibrePoincare.ginibreWeakCoreGraph","GinibrePoincare.ginibreWeakCoreGraph_isClosed","GinibrePoincare.polynomialEigenfunctionL2","GinibrePoincare.polynomialEigenfunction_full_core_weak_equation","GinibrePoincare.polynomialEigenfunction_full_core_weak_equation._proof_2","GinibrePoincare.polynomialEigenfunction_mem_closedGenerator_domain","GinibrePoincare.polynomialGeneratorGraph","GinibrePoincare.polynomialGeneratorGraph._proof_1","GinibrePoincare.polynomialGeneratorGraph._proof_2","GinibrePoincare.polynomialGeneratorGraph._proof_4","GinibrePoincare.polynomialGeneratorGraph._proof_5","GinibrePoincare.polynomialGeneratorGraph._proof_6","GinibrePoincare.polynomialGeneratorRate","HSMul.hSMul","Iff.mpr","Inner.inner","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearPMap.domain","LinearPMap.graph","LinearPMap.toFun'","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup"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","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.preimage","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_nonneg","addRightReflectLE_of_addLeftReflectLE","congrArg","continuous_id","contravariant_lt_of_covariant_le","dist_zero_right","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instTransLE","isClosed_tsupport","le_abs_self","le_of_lt","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","mul_pos_of_neg_of_neg","neg_eq_zero","neg_neg_of_pos","norm_le_pi_norm","pi_norm_le_iff_of_nonneg","pi_properSpace","propext","pseudoMetricSpacePi","rfl","sub_eq_zero_of_eq","tsupport","tsupport_comp_subset_preimage"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDistributionalGradient","name":"GinibrePoincare.compactSupport_collisionFree_test_div_density_sq","type_dependencies":["Complex","Complex.instNormedField","DivInvMonoid.toDiv","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","HDiv.hDiv","HPow.hPow","HasCompactSupport","Monoid.toNPow","NPow.toPow","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHDiv","instHPow","instOfNatNat"],"value_dependencies":["Complex","Complex.instNormedField","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.trans","Field.toSemifield","Fin","Function.support","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HPow.hPow","HasCompactSupport","HasCompactSupport.mono","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instField","Real.instMonoid","Real.instZero","Semifield.toDivisionSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","instHDiv","instHPow","instOfNatNat","of_eq_true","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIReduction","name":"GinibrePoincare.compactSupport_gaussian_radial_lift","type_dependencies":["Complex","Complex.instNormedField","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.gaussianBlockRadii","HAdd.hAdd","HasCompactSupport","LT.lt","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.instZero","Complex.normSq","Complex.normSq_eq_norm_sq","Complex.normSq_nonneg","ContDiff.continuous","Continuous","Continuous.continuousOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.mem_univ","Finset.single_le_sum","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.Configuration","G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NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.ComplexGaussianDensity","name":"GinibrePoincare.complexCoordinateGaussianDensity","type_dependencies":["Complex","ENNReal","Nat"],"value_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","ENNReal.ofReal","HDiv.hDiv","HMul.hMul","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","Neg.neg","Real","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.pi","Real.semiring","instHDiv","instHMul","instMulZeroOneClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianDensity","name":"GinibrePoincare.complexCoordinateGaussianDensity.eq_1","type_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.ofReal","Eq","GinibrePoincare.complexCoordinateGaussianDensity","HDiv.hDiv","HMul.hMul","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","Neg.neg","Real","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.pi","Real.semiring","instHDiv","instHMul","instMulZeroOneClassOfSemiring"],"value_dependencies":["Complex","ENNReal","Eq.refl","GinibrePoincare.complexCoordinateGaussianDensity","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.complexCoordinateGaussianDensity_globalPhase","type_dependencies":["Complex","Complex.instMul","Complex.instNorm","ENNReal","Eq","GinibrePoincare.complexCoordinateGaussianDensity","HMul.hMul","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","instHMul"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","CommRing.toNonUnitalCommRing","Complex","Complex.instMul","Complex.instNorm","Complex.instSemiring","Complex.normSq","Complex.normSq_mul","Complex.sq_norm","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.ofReal","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.complexCoordinateGaussianDensity","HDiv.hDiv","HMul","HMul.hMul","HPow.hPow","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAddMonoidWithOne","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.commRing","Real.exp","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRing","Real.pi","Real.semiring","Ring.toAddGroupWithOne","True","True.intro","congr","congrArg","congrFun'","eq_self","eq_true","id","instHDiv","instHMul","instHPow","instMulZeroOneClassOfSemiring","instOfNatNat","neg_mul","of_eq_true","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianMoments","name":"GinibrePoincare.complexCoordinateGaussianDensity_toReal","type_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","ENNReal.toReal","Eq","GinibrePoincare.complexCoordinateGaussianDensity","HDiv.hDiv","HMul.hMul","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","Neg.neg","Real","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.pi","Real.semiring","instHDiv","instHMul","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal.ofReal","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mpr","Eq.refl","Field.toSemifield","GinibrePoincare.complexCoordinateGaussianDensity","HDiv.hDiv","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_nonneg'","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.to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oidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.ext","Complex.im","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.inv_I","Complex.inv_im","Complex.inv_re","Complex.measurableSpace","Complex.mul_im","Complex.mul_re","Complex.normSq","Complex.normSq_ofNat","Complex.ofReal","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Filter.univ_mem'","Fin","Finsupp","Finsupp.instAddZeroClass","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.contDiff_diagonalEvalPublic","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.diagonalEvalPublic","GinibrePoincare.ComplexHermite.exists_fderiv_diagonalEvalPublic_polynomial","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianDbarIntegrationByParts_of_integrable","GinibrePoincare.integrable_conj_mul_mvPolynomial_diagonalEval","GinibrePoincare.integrable_mul_mvPolynomial_diagonalEval","GinibrePoincare.integrable_mvPolynomial_diagonalEval","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvolutiveNeg.toNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Matrix.vecCons","Matrix.vecEmpty","MeasureTheory.Integrable","MeasureTheory.Integrable.add","MeasureTheory.Integrable.congr","MeasureTheory.Integrable.const_mul","MeasureTheory.Integrable.sub","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ProbabilityMeasure.toMe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inibrePoincare.integrable_realProd_of_integrable_complexGaussian","GinibrePoincare.integral_complexGaussian_eq_integral_prod","GinibrePoincare.realCoordinateGaussianProbability","GinibrePoincare.realGaussianIntegrationByParts_of_gaussian_integrable","HAdd.hAdd","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.AEStronglyMeasurable","MeasureTheory.HasFiniteIntegral","MeasureTheory.Integrable","MeasureTheory.Integrable.congr","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.ProbabilityMeasure.instIsProbabilityMeasureToMeasure","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.ae","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integrable_prod_iff","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const_mul","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.denselyNormedField","Real.instAdd","Real.instAddMonoid","Real.instCompleteSpace","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","deriv","eq_self","fderiv","funext","id","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","mul_one","of_eq_true","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.complexGaussianIntegrationByParts_real","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.re","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","GinibrePoincare.complexCoordinateGaussianProbability","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedFiel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orelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal.ofReal","Eq","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianLebesgueDensityReal","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","OfNat.ofNat","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal.ofReal","Eq","Eq.mpr","Eq.refl","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianDensityIdentification","GinibrePoincare.complexGaussianDensityMeasure","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianLebesgueDensityReal","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","OfNat.ofNat","congrArg","id","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.complexGaussianMeasure_isOpenPosMeasure","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","IsOpen","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Nonempty","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroupWithOne.toAddGroup","BorelSpace.opensMeasurable","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","Eq","Eq.mpr","Eq.trans","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.support","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianDensity","GinibrePoincare.complexGaussianDensityIdentification","GinibrePoincare.complexGaussianDensityMeasure","GinibrePoincare.complexGaussianDensityMeasure.eq_1","GinibrePoincare.complexGaussianDensity_pos","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationVolume","GinibrePoincare.configurationVolume.eq_1","GinibrePoincare.measurable_complexGaussianDensity","Iff","Inter.inter","IsOpen","IsOpen.measurableSet","IsOpen.measure_pos","LT.lt","LT.lt.ne'","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsOpenPosMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","MeasureTheory.setLIntegral_pos_iff","MeasureTheory.withDensity_apply","Membership.mem","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.Nonempty","Set.ext","Set.instInter","Set.instMembership","Set.univ","Set.univ_inter","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreMassPositivity.0.GinibrePoincare.complexGaussianMeasure_isOpenPosMeasure._simp_1_3","_private.GinibrePoincare.Analysis.GinibreMassPositivity.0.GinibrePoincare.complexGaussianMeasure_isOpenPosMeasure._simp_1_4","congr","congrArg","id","iff_true","instCountableFin","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLTNat","instOfNat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ommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","congr","congrArg","eq_self","id","instDistribOfSemiring","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","integral_conj","map_mul","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2PiProducts","name":"GinibrePoincare.complexLp_integral_norm_sq","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNorm","Complex.instNormedAddCommGroup","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","HPow.hPow","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","HPow.hPow","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","congrArg","eq_self","fact_one_le_two_ennreal","funext","id","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","real_inner_self_eq_norm_sq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialLpConjugation","name":"GinibrePoincare.complexLp_norm_star","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing",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rePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.complexMulMeasurableEquiv._proof_9","type_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.instZero","Eq","HMul.hMul","Inv.inv","Ne","OfNat.ofNat","Zero.toOfNat0","instHMul"],"value_dependencies":["Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Complex","Complex.instField","Complex.instInv","Complex.instMul","Complex.instZero","Decidable.decide","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Ne","NeZero.one","Neg.neg","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.mk","Prod.snd","Semifield.toCommGroupWithZero","True","Zero.toOfNat0","congrArg","congr_arg","congr_arg\u2082","div_one","eq_self","id","inferInstance","instHDiv","instHMul","instIsCancelMulZero","instOfNat","mul_one","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralRadialProjectionPhase","name":"GinibrePoincare.complexMulMeasurableEquiv.congr_simp","type_dependencies":["Complex","Complex.instZero","Complex.measurableSpace","Eq","Eq.ndrec","GinibrePoincare.complexMulMeasurableEquiv","MeasurableEquiv","Ne","OfNat.ofNat","Zero.toOfNat0"],"value_dependencies":["Complex","Complex.instZero","Complex.measurableSpace","Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.complexMulMeasurableEquiv","MeasurableEquiv","Ne","OfNat.ofNat","Zero.toOfNat0"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.complexMultiplicationMatrix","type_dependencies":["Complex","Fin","Matrix","Nat","OfNat.ofNat","Real","instOfNatNat"],"value_dependencies":["Complex","Complex.im","Complex.re","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Matrix","Matrix.of","Matrix.vecCons","Matrix.vecEmpty","Nat","Neg.neg","OfNat.ofNat","Real","Real.instNeg","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.complexMultiplicationMatrix.eq_1","type_dependencies":["Complex","Complex.im","Complex.re","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.complexMultiplicationMatrix","Matrix","Matrix.of","Matrix.vecCons","Matrix.vecEmpty","Nat","Neg.neg","OfNat.ofNat","Real","Real.instNeg","instOfNatNat"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.complexMultiplicationMatrix","Matrix","Nat","OfNat.ofNat","Real","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixPolynomialNull","name":"GinibrePoincare.complexMvPolynomial_eval_ne_zero_ae","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instZero","Complex.measurableSpace","DFunLike.coe","Filter.Eventually","Finsupp","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Fintype","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.NullSingletonClass","MeasureTheory.SigmaFinite","MeasureTheory.ae","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","OfNat.ofNat","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AlgEquiv","AlgEquiv.injective","AlgEquiv.instFunLike","AlgHom","AlgHom.funLike","Algebra.i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oidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_apply","Finset.sum_ite_eq","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.complexRadius_eq","GinibrePoincare.coordinateDirection","GinibrePoincare.fderiv_complexRadius","GinibrePoincare.radiusBilinear","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","fderiv","funext","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_left_of_eq_true","map_sum","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.complexRadius_coordinateDirection","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instStarRing","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.coordinateDirection","GinibrePoincare.coordinateSum","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toModule","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_congr","Finset.sum_ite_eq'","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.coordinateDirection","GinibrePoincare.coordinateSum","GinibrePoincare.fderiv_complexRadius","GinibrePoincare.radiusBilinear","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","NNRat","NPow.toPow","Nat","Nat.cast","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","RingHomClass.toMonoidWithZeroHomClass","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","apply_ite","congr","congrArg","congrFun'","fderiv","funext","id","inferInstance","instCommSemiringNNRat","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","ite","ite_congr","ite_eq_left_of_eq_true","ite_mul","map_sum","map_zero","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.complexRadius_coulomb","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.coulombPairDirection","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing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RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","congrArg","id","instMulZeroClassOfSemiring","smulCommClass_self","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticFiniteProjection","name":"GinibrePoincare.complexSuccessiveProjections_commutes","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.comp","Eq","GinibrePoincare.complexSuccessiveProjections","InnerProductSpace","InnerProductSpace.toNormedSpace","List","List.instMembership","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp_assoc","ContinuousLinearMap.comp_id","ContinuousLinearMap.id_comp","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.complexSuccessiveProjections","InnerProductSpace","InnerProductSpace.toNormedSpace","List","List.cons","List.instMembership","List.mem_cons_of_mem","List.mem_cons_self","List.nil","List.rec","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","congr","congrArg","eq_self","id","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticFiniteProjection","name":"GinibrePoincare.complexSuccessiveProjections_error","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.adjoint","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","EquivLike.toFunLike","Field.toCommRing","Field.toSemifield","GinibrePoincare.complexSuccessiveProjections","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","LE.le","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","List","List.instMembership","List.map","List.sum","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instAdd","Real.instLE","Real.instMonoid","Real.instOne","Real.instZero","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologic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ibrePoincare.configurationFourierCharacter","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.configurationFourierCharacter_add","type_dependencies":["Complex","Complex.instAdd","Complex.instMul","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","HAdd.hAdd","HMul.hMul","Nat","Pi.instAdd","instHAdd","instHMul"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","CommSemiring.toSemiring","Complex","Complex.I","Complex.exp","Complex.exp_add","Complex.instAdd","Complex.instCommSemiring","Complex.instMul","Complex.ofReal","Complex.ofReal_add","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","GinibrePoincare.configurationRealPairing_add","HAdd.hAdd","HMul.hMul","HPow.hPow","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Pi.instAdd","Real","Real.instAdd","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","congrFun'","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.configurationFourierCharacter_zero","type_dependencies":["Complex","Complex.instOne","Complex.instZero","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","Nat","OfNat.ofNat","One.toOfNat1","Pi.instZero","Zero.toOfNat0"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.I","Complex.exp","Complex.exp_zero","Complex.im","Complex.instMul","Complex.instOne","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.re","Eq","Eq.refl","Eq.trans","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const_zero","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","HAdd.hAdd","HMul.hMul","Membership.mem","MulZeroClass.toZero","MulZeroClass.zero_mul","Nat","OfNat.ofNat","One.toOfNat1","Pi.instZero","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instMul","Real.semiring","SetLike.instMembership","True","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_self","instHAdd","instHMul","instMulZeroClassOfSemiring","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.configurationGaussianDbarIntegrationByParts","type_dependencies":["Complex","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instOneENat"],"value_dependencies":["Complex","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.ndrec","Eq.symm","Exists","Exists.casesOn","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoi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","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","Submodule"],"value_dependencies":["CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instSemiring","Complex.instStarRing","DFunLike.coe","Eq","Exists","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","HMul.hMul","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Pi.Function.module","Pi.addCommMonoid","RingHom","RingHom.instFunLike","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.ofPred","Submodule.span","instHMul","instHPow","starRingEnd"]},{"kind":"definition","module":"GinibrePoincare.Concrete.Weights","name":"GinibrePoincare.configurationNormSq","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Real","Real.instAddCommMonoid","Real.semiring","instMulZeroOneClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianDensity","name":"GinibrePoincare.configurationNormSq.eq_1","type_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","Eq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Real","Real.instAddCommMonoid","Real.semiring","instMulZeroOneClassOfSemiring"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreSpatialCutoffs","name":"GinibrePoincare.configurationNormSq_gradient_norm_sq","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibreEuclideanGradient","HMul.hMul","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.instNorm","Prod","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.norm","instFintypeProd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.mul_re","Complex.normSq","Complex.normSq_apply","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","False","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Fin.sum_univ_two","Finset","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.sum_eq_single","Finset.univ","Fintype.sum_prod_type","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.fderiv_configurationNormSq_apply","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_coordinate","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsEmpty.forall_iff._simp_1","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_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.instNormedField","IsTopologicalSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Field.toDivisionRing","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialCompactApproximation","name":"GinibrePoincare.configurationPolynomialStarAlgebra._proof_2","type_dependencies":["Algebra.id","Algebra.toSMul","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instSemiring","ContinuousConstSMul","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Algebra.id","Complex","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","ContinuousMap.algebra._proof_3","Field.toDivisionRing","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialCompactApproximation","name":"GinibrePoincare.configurationPolynomialStarAlgebra._proof_3","type_dependencies":["AddCommMonoid.toAddMonoid","Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","ContinuousMap","ContinuousMap.instSMul","ContinuousMap.instStar","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationPolynomialStarAlgebra._proof_2","InvolutiveStar.toStar","Membership.mem","Nat","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarModule","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoid.toAddMonoid","Algebra.id","Algebra.toSMul","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","ContinuousMap.algebra._proof_3","ContinuousMap.instStarModule","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","InvolutiveStar.toStar","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","Membership.mem","Nat","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarMul.toStarModule","StarRing.toStarAddMonoid","StarRing.toStarMul","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.Poly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italNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.addZeroClass","Pi.distribSMul","Pi.instAdd","Pi.instZero","Rat.rawCast","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.add_mem","Submodule.setLike","Submodule.smul_mem","Submodule.subset_span","Submodule.sum_mem","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","add_zero","apply_ite","congr","congrArg","congrFun","congrFun'","div_self_mul_self'","eq_self","funext","id","inferInstance","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","ite","ite_congr","ite_eq_left_of_eq_true","mul_neg","mul_one","neg_mul","neg_zero","of_eq_true","one_mul","pow_one","pow_zero","rfl","smul_add","starRingEnd","sub_neg_eq_add","sub_zero","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.configurationRealPairing_realScale","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.configurationRealPairing","GinibrePoincare.realScaleConfiguration","HMul.hMul","Nat","Real","Real.instMul","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.im","Complex.instMul","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationRealPairing","GinibrePoincare.realScaleConfiguration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","MulZeroClass.zero_mul","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instRing","Real.instSub","Real.semiring","Ring.toAddGroupWithOne","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congr","congrArg","congrFun'","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","rfl","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevSpatialTruncation","name":"GinibrePoincare.configurationSpatialCutoff_L2_errors_tendsto","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","And","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","EN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Group","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","And","And.casesOn","And.intro","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.instT2Space","Complex.measurableSpace","Complex.re","Complex.reCLM","ContDiff","ContDiff.comp","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiff.sub","Continuous","Continuous.clm_apply","Continuous.comp","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp.congr_simp","ContinuousLinearMap.comp_id","ContinuousLinearMap.comp_neg","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.lsmul","ContinuousLinearMap.neg","ContinuousLinearMap.ring","ContinuousLinearMap.sub","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.configuration_scalar_convolution_derivative","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_homeomorph","HasCompactSupport.fderiv_apply","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","HasFDerivAt.sub","Homeomorph.subLeft","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsModuleTopology.toContinuousSMul","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","MeasureTheory.integral","MeasureTheory.integral_add","MeasureTheory.integral_neg","MeasureTheory.integral_sub","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","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_prod","type_dependencies":["Complex","Complex.instNorm","Complex.instNormedField","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","HAdd.hAdd","LE.le","Nat","Norm.norm","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toNorm","OfNat.ofNat","One.toOfNat1","Pi.normedRing","Real","Real.instAdd","Real.instCommMonoid","Real.instLE","Real.instOne","instHAdd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommMonoid.toMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNorm","Complex.instNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.mem_univ","Finset.mul_prod_erase","Finset.one_le_prod\u2080","Finset.prod","Finset.univ","Function.swap","GinibrePoincare.Configuration","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_mul_eq","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toNorm","NormedRing.toSeminormedRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.normedRing","Pi.seminormedAddGroup","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommMonoid","Real.instCommMonoidWithZero","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedRing.toNonUnitalSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZer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Monoid","SubtractionMonoid.toSubNegZeroMonoid","T5Space.toT1Space","T6Space.toT5Space","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.pseudoMetrizableSpace_prod","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","add_pos'","congrArg","continuous_add","continuous_apply","id","inferInstance","instAddNat","instCountableFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instPerfectSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","inv_le_inv\u2080","inv_pos_of_pos","le_of_lt","le_of_not_gt","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_inv","mul_pos","norm_pos_iff","pow_pos","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.configuration_real_basis_expansion","type_dependencies":["Algebra.toSMul","Complex","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRCLike","Complex.re","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HSMul.hSMul","Nat","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Pi.addCommMonoid","Pi.instAdd","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instHAdd","instHSMul"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.re","Complex.re_add_im","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.refl","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_add_distrib","Finset.sum_apply","Finset.sum_congr","Finset.sum_ite_eq","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Membership.mem","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.addCommMonoid","Pi.instAdd","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","SetLike.instMembership","True","Zero.toOfNat0","congr","congrArg","congrFun","eq_self","funext","instDecidableEqFin","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","ite","ite_congr","ite_eq_left_of_eq_true","mul_one","of_eq_true","smul_ite","smul_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointMollification","name":"GinibrePoincare.configuration_scalar_convolution_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","ContDiff","ContDiff.continuous_fderiv","ContDiff.of_le","ContinuousAdd.measurableAdd","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.integral_apply","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.precompL","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.topologicalSpace","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.trans","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.convolutionExists_left","HasCompactSupport.fderiv","HasCompactSupport.hasFDerivAt_convolution_left","HasFDerivAt","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","MeasureTheory.ConvolutionExistsAt.integrable_swap","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.Pi.isAddLeftInvariant_volume","MeasureTheory.Pi.isNegInvariant_volume","MeasureTheory.convolution","MeasureTheory.convolution_eq_swap","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integral","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toMulOneClass","Monoid.t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orelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","HAdd.hAdd","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHAdd","instHMul","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiff.mul","Continuous.clm_apply","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.differentiableAt","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.local_integrable_mul_compact_test","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Commo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ing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.contDiffAt_log","Real.denselyNormedField","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.log","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","contDiffAt_const","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.contDiffOn_ginibreLebesgueDensityReal_collisionFree","type_dependencies":["Compl.compl","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiffOn","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.ginibreLebesgueDensityReal","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instCompl","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Compl.compl","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.contDiffOn","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.contDiff_ginibreLebesgueDensityReal","GinibrePoincare.ginibreLebesgueDensityReal","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instCompl","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDistributionalGradient","name":"GinibrePoincare.contDiff_collisionFree_test_div_density_sq","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","HDiv.hDiv","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.ofPred","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instHDiv","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopENat","tsupport"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.contDiffAt","ContDiffAt","ContDiffAt.congr_of_eventuallyEq","ContDiffAt.div","ContDiffAt.pow","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENat","Eq","Eq.trans","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.contDiff_ginibreLebesgueDensityReal","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreLebesgueDensityReal_ne_zero_of_collisionFree","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HPow.hPow","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.decidableEq","Real.denselyNormedField","Real.instDivInvMonoid","Real.instField","Real.instMonoid","Real.instMonoidWithZero","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","congrFun'","contDiffAt_const","contDiff_iff_contDiffAt","dite","eq_self","id","instHDiv","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopENat","isReduced_of_noZeroDivisors","nhds","notMem_tsupport_iff_eventuallyEq","of_eq_true","pow_ne_zero","tsupport","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.contDiff_comp_complexImagSlice","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.complexImagSlice","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.ofReal","Complex.ofRealCLM","ContDiff","ContDiff.add","ContDiff.comp","ContDiff.mul","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","GinibrePoincare.complexImagSlice","HMul.hMul","InnerProductSpace.toNormedSpace","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","contDiff_const","id","instHMul","instInnerProductSpaceRealComplex","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.contDiff_comp_complexRealSlice","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.complexRealSlice","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.instMul","Complex.instNormedAddCommGroup","Complex.ofReal","Complex.ofRealCLM","ContDiff","ContDiff.add","ContDiff.comp","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","GinibrePoincare.complexRealSlice","HMul.hMul","InnerProductSpace.toNormedSpace","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.in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iviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","Not","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.decidableEq","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Real.smoothTransition","Real.smoothTransition.contDiff","Real.smoothTransition.nonneg","Real.smoothTransition.one_of_one_le","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","WithTop.some","Zero.toOfNat0","add_pos_of_pos_of_nonneg","congr","congrArg","congrFun'","contDiff_const","dite","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","lt_of_le_of_ne","mul_nonneg","mul_one","sub_zero","zero_add","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianRadialGenerator","name":"GinibrePoincare.contDiff_ginibreCenterSquared","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquared","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["GinibrePoincare.ginibre_contDiff_center_normSq","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.contDiff_ginibreDirectionalFlux_core","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreLebesgueDensityReal","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","And","And.left","CommSemiring.toSemiring","Compl.compl","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.comp","ContDiff.contDiff_fderiv_apply","ContDiff.mul","ContDiff.prodMk","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNi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omplex.instRCLike","Complex.ofReal","Complex.ofRealCLM","ContDiff","ContDiff.comp","ContDiff.mul","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","ENat","Eq","Eq.mpr","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.contDiff_vandermonde","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.normalizedVandermondeTransform_apply","GinibrePoincare.vandermonde","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","Nat","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","congrArg","contDiff_const","funext","id","instDistribOfSemiring","instHMul","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorWeakCore","name":"GinibrePoincare.contDiff_polynomialEigenfunction","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunction","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AlgHom","AlgHom.funLike","Algebra.id","Bool","Bool.true","CommSemiring.toSemiring","Complex","Complex.conjCLE","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.normSq","Complex.ofReal","Complex.ofRealCLM","Complex.re","Complex.reCLM","ContDiff","ContDiff.add","ContDiff.comp","ContDiff.mul","ContDiff.pow","ContDiff.sub","ContDiff.sum","ContinuousLinearEquiv","ContinuousLinearEquiv.contDiff","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instOfNat","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Function.comp","GinibrePoincare.ComplexHermite.Poly","GinibrePoincare.ComplexHermite.W","GinibrePoincare.ComplexHermite.Z","GinibrePoincare.ComplexHermite.Z._proof_1","GinibrePoincare.ComplexHermite.normalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.ComplexHermite.raw","GinibrePoincare.ComplexHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.Laguerre.polynomial","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.R_poly","GinibrePoincare.S_observable","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","GinibrePoincare.pairwiseRadius","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","LT.lt","Matrix.vecCons","Matrix.vecEmpty","Membership.mem","Min.min","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHomClass.toMonoidHomClass","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.decLt","Nat.factorial","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","Neg.neg","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.contDiff_aeval","Polynomial.eval","Polynomial.eval\u2082","Polynomial.semiring","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instCommSemiring","Real.instInv","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","congr","congrArg","congrFun'","contDiff_apply","contDiff_const","contDiff_id","funext","id","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instMinNat","instMulZeroOneClassOfSemiring","instOfNatNat","instSubNat","instTopENat","map_mul","map_pow","map_sum","of_decide_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.contDiff_vandermonde","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","ContDiff","ContDiff.sub","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.mpr","Eq.refl","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.instSetLike","Finset.prod","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","GinibrePoincare.vandermonde_eq_product","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","Nat","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnital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ilbertBasis.repr","Iff.mp","InnerProductSpace.toNormedSpace","Int","Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.injective","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.instSemilinearIsometryEquivClass","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_zero","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instZero","PreLp","PreLp.instAddCommGroup","PreLp.instAddCommMonoid","PreLp.ring","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","QuotientAddGroup.Quotient.addGroup","QuotientAddGroup.borelSpace","QuotientAddGroup.instTopologicalSpace","QuotientAddGroup.measurableSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.borelSpace","Real.instAddCommGroup","Real.instAddCommSemigroup","Real.instCompleteSpace","Real.instLT","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearIsometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","T5Space.toT1Space","T6Space.toT0Space","T6Space.toT5Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun","congrFun'","continuous_const","eq_self","fact_one_le_two_ennreal","fourierBasis","fourierBasis_repr","fourierCoeff","fourierCoeff_toLp","funext","id","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","lp","lp.ext","lp.instModuleSubtypePreLpMemAddSubgroup","lp.normedAddCommGroup","map_zero","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralRadialProjectionFourier","name":"GinibrePoincare.continuous_circle_mem_closed_span_fourierCoeff","type_dependencies":["AddCircle","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddSubgroup.zmultiples","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Com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edAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set.mem_range_self","Set.range","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.inner_left_of_mem_orthogonal","Submodule.mem_orthogonal'","Submodule.orthogonal","Submodule.orthogonal_orthogonal_eq_closure","Submodule.setLike","Submodule.span","Submodule.subset_span","Submodule.topologicalClosure","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T5Space.toT1Space","T6Space.toT0Space","T6Space.toT5Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","continuous_const","fourier","fourierCoeff","fourierCoeff.eq_1","funext","id","innerSL","inner_eq_zero_symm","inner_smul_right","instDistribOfSemiring","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexSquaredGradient","name":"GinibrePoincare.continuous_complexDirectionalEnergy","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.complexDirectionalEnergy","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.continuous_normSq","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.normSq","ContDiff","ContDiff.continuous_fderiv","Continuous.clm_apply","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","continuous_const","continuous_finsetSum","fderiv","instFintypeProd","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instOfNatNat","instTopENat","instZeroENat","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.continuous_configurationFourierCharacter","type_dependencies":["Complex","Complex.instNormedField","Continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.I","Complex.continuous_exp","Complex.continuous_ofReal","Complex.exp","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.ofReal","Continuous","Continuous.comp","Continuous.mul","Field.toDivisionRing","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","GinibrePoincare.continuous_configurationRealPairing_left","HMul.hMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_const","id","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.continuous_configurationRealPairing_left","type_dependencies":["Complex","Complex.instNormedField","Continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationRealPairing","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","Complex","Complex.continuous_im","Complex.continuous_re","Complex.im","Complex.instNormedField","Complex.re","Continuous","Continuous.comp'","Continuous.const_mul","Continuous.prodMk","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationRealPairing","HAdd.hAdd","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","continuous_add","continuous_apply","continuous_finsetSum","id","instHAdd","instHMul","instIsTopologicalRingReal","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.continuous_correspondenceOperatorEvolution","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instTopologicalSpace","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.continuous_resolventCfcEvolution","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorComplexResolvent_denseRange","GinibrePoincare.correspondenceOperatorComplexResolvent_isSelfAdjoint","GinibrePoincare.correspondenceOperatorComplexResolvent_spectrum","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.continuous_dbarComponent","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","ContDiff","ContDiff.continuous_fderiv","Continuous","Continuous.add","Continuous.clm_apply","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq.refl","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat","Nat.cast_one","Nat.cast_zero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOneENat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.L2RepresentativeBridges","name":"GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","Eq","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instT2Space","Complex.measurableSpace","Continuous","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.measurableSpace","ENNReal.ofReal","ENNReal.ofReal_pos","Eq","Eq.mpr","Field.toSemifield","Filter.EventuallyEq","Filter.univ_mem'","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianDensity","GinibrePoincare.complexGaussianDensityIdentification","GinibrePoincare.complexGaussianDensityMeasure","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.configurationVolume","GinibrePoincare.gaussianWeight","GinibrePoincare.measurable_complexGaussianDensity","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.IsOpenPosMeasure","MeasureTheory.Measure.eq_of_ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsOpenPosMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.withDensity_absolutelyContinuous'","Membership.mem","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Ne","NeZero.charZero_one","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.pi","Real.pi_pos","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoidWithZero","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","div_pos","id","inferInstance","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_pos","ne_of_gt","pow_pos","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMagnitudeProfile","name":"GinibrePoincare.continuous_gammaMagnitudes","type_dependencies":["Continuous","Fin","GinibrePoincare.gammaMagnitudes","Nat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous","Continuous.comp'","Continuous.div_const","Continuous.sqrt","DivInvMonoid.toDiv","Fin","GinibrePoincare.gammaMagnitudes","HDiv.hDiv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instDivInvMonoid","Real.instNatCast","Real.pseudoMetricSpace","Real.sqrt","UniformSpace.toTopologicalSpace","continuous_apply","continuous_id'","continuous_pi","id","instHDiv","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireRepresentatives","name":"GinibrePoincare.continuous_gaussianAlternating_representative","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","Continuous.comp","Continuous.mul","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Equiv.instEquivLike","EquivLike.toFunLike","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianAlternatingL2._proof_4","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.gaussianPermutationL2._proof_1","GinibrePoincare.gaussianPermutationL2._proof_2","GinibrePoincare.gaussianSymmetricL2._proof_4","GinibrePoincare.gaussianSymmetricL2._proof_5","GinibrePoincare.gaussian_measurePreserving_permute","GinibrePoincare.permutationSign","GinibrePoincare.permute","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instMul","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","congrFun","continuous_apply","continuous_const","continuous_pi","fact_one_le_two_ennreal","id","instHMul","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianBlockRadialLaw","name":"GinibrePoincare.continuous_gaussianBlockRadius","type_dependencies":["Complex","Complex.instNormedField","Continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.gaussianBlockRadius","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","Complex","Complex.continuous_normSq","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Continuous","Continuous.comp'","Continuous.const_mul","DFunLike.coe","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianBlockRadius","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","continuous_apply","continuous_finsetSum","id","instHMul","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDirectionalDerivative","name":"GinibrePoincare.continuous_gaussianCircleDerivativeKernel","type_dependencies":["Complex","Complex.instNormedField","Continuous","GinibrePoincare.gaussianCircleDerivativeKernel","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","Bool","Bool.false","CommGroupWithZero.toDivisionCommMonoid","Complex","Complex.I","Complex.addCommGroup","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.instSub","Complex.instZero","Continuous","Continuous.mul","Continuous.pow","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gaussianCircleDerivativeKernel","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","InvOneClass.toInv","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_ofNat","Metric.mem_ball_self","Monoid.toNPow","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","Pi.instMul","Pi.instPow","PseudoMetricSpace.toUniformSpace","Real","Real.instFloorRing","Real.instIsOrderedRing","Real.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","circleMap","congrArg","continuous_circleMap","continuous_circleMap_inv","continuous_const","eq_of_heq","eq_self","funext","id","instHMul","instHPow","instHSub","instOfNatNat","inv_pow","of_eq_true","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDistance","name":"GinibrePoincare.continuous_gaussianL2_iff_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianL2","GinibrePoincare.complexGaussianMeasure","Iff","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.sq_norm","Continuous","Continuous.aestronglyMeasurable","ContinuousENorm.toENorm","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianL2","GinibrePoincare.complexGaussianMeasure","HPow.hPow","Iff","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.memLp_two_iff_integrable_sq_norm","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","True","UniformSpace.toTopologicalSpace","autoParam","congrArg","congrFun'","funext","id","iff_self","instCountableFin","instHPow","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","propext","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevClosure","name":"GinibrePoincare.continuous_ginibreEuclideanGradient","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreEuclideanGradient","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.continuous_fderiv","Continuous","Continuous.clm_apply","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype",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roup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.continuous_resolventCfcEvolution","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_denseRange","GinibrePoincare.ginibreFullComplexResolvent_isSelfAdjoint","GinibrePoincare.ginibreFullComplexResolvent_spectrum","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupPaperSpeed","name":"GinibrePoincare.continuous_ginibreFullPaperEvolution","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullPaperEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instTopologicalSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup",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edCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Polynomial.coeff","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instOne","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","continuous_const","continuous_finsetSum","id","instDecidableEqFin","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instTopologicalSpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevContinuity","name":"GinibrePoincare.continuous_matrix_charpoly_coeff","type_dependencies":["CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instNormedField","Continuous","DFunLike.coe","Fin","Fin.fintype","Finsupp","Finsupp.instFunLike","Matrix","Matrix.charpoly","MulZeroClass.toZero","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Polynomial.coeff","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDecidableEqFin","instMulZeroClassOfSemiring","instTopologicalSpaceMatrix"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNontrivial","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","Continuous","Continuous.const_mul","Continuous.matrix_det","Continuous.matrix_submatrix","DFunLike.coe","Decidable.byContradiction","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.trans","Field.toDivisionRing","Fin","Fin.fintype","Finset","Finset.Subtype.fintype","Finset.instSetLike","Finset.powersetCard","Finset.sum","Finset.univ","Finsupp","Finsupp.instFunLike","Fintype.card","Fintype.card_fin","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Matrix","Matrix.charpoly","Matrix.charpoly_coeff_eq_sum_minors","Matrix.charpoly_natDegree_eq_dim","Matrix.det","Matrix.submatrix","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.decLe","Nat.decLt","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.sub_sub_self","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","One.toOfNat1","Polynomial.coeff","Polynomial.coeff_eq_zero_of_natDegree_lt","Polynomial.natDegree","PseudoMetricSpace.toUniformSpace","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toMonoid","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.instDecidableEq","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.MatrixSpectralSobolevContinuity.0.GinibrePoincare.continuous_matrix_charpoly_coeff._proof_1_1","congrArg","congrFun'","continuous_const","continuous_finsetSum","continuous_id'","contravariant_lt_of_covariant_le","dite","funext","id","instAddNat","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLENat","instLTNat","instMulZeroClassOfSemiring","instSubNat","instTopologicalSpaceMatrix","le_add_iff_nonneg_right._simp_1","of_eq_true","tsub_le_iff_right._simp_1","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralVanishingAmplitude","name":"GinibrePoincare.continuous_mul_punctured_of_initial_zero","type_dependencies":["Continuous","ContinuousOn","Eq","HMul.hMul","LE.le","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Norm.norm","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMul","Real.instZero","Real.norm","Real.pseudoMetricSpace","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddGroup.toSubtractionMonoid","CommRing.toNonUnitalCommRing","Continuous","Continuous.continuousAt","Continuous.norm","ContinuousAt","ContinuousAt.mul","ContinuousAt.mul_const","ContinuousOn","ContinuousOn.continuousAt","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","Filter","Filter.Tendsto","HMul.hMul","Iff.mpr","IsOpen.mem_nhds","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","MulZeroClass.toZero","MulZeroClass.zero_mul","NNReal","NNReal.instLinearOrder","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Ne.symm","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","OrderTopology.to_orderClosedTopology","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Real.norm","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Ioi","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","bot_le","congrArg","congrFun'","continuous_iff_continuousAt","dite","id","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","isOpen_Ioi","lt_of_le_of_ne","mul_le_mul_of_nonneg_left","nhds","norm_mul","norm_nonneg","norm_zero","squeeze_zero","tendsto_zero_iff_norm_tendsto_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.continuous_planarL2Translate","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace.opensMeasurable","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instField","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","Continuous.comp","Continuous.vadd","ContinuousAdd.measurableAdd","ContinuousNeg.continuous_neg","DFunLike.coe","DomAddAct","DomAddAct.continuous_mk","DomAddAc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Fun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instTopologicalSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.continuous_ofReal","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Continuous","Continuous.comp'","Continuous.const_mul","Continuous.fun_const_smul","Continuous.fun_smul","Continuous.rexp","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instFunLike","Finsupp.module","Finsupp.support","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorCombination","GinibrePoincare.polynomialSectorEigenvector","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorEvolution","GinibrePoincare.polynomialSectorEvolution_combination","GinibrePoincare.polynomialSectorFiniteEvolution","GinibrePoincare.polynomialSectorFiniteEvolution._proof_1","GinibrePoincare.polynomialSectorFiniteEvolution._proof_4","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","MulZeroClass.toZero","NNReal","NNReal.continuous_coe","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGro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funext","id","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EntireVandermondeDivision","name":"GinibrePoincare.continuous_vandermonde_quotient_symmetric","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Continuous","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.IsSymmetric","GinibrePoincare.vandermonde","HMul.hMul","LT.lt","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toIntCast","Complex","Complex.addGroupWithOne","Complex.instCharZero","Complex.instField","Complex.instIntCast","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Continuous","Continuous.comp","DFunLike.coe","DivInvMonoid.toMonoid","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Equiv.Perm","Equiv.Perm.permGroup","Equiv.Perm.sign","Equiv.instEquivLike","EquivLike.toFunLike","False","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.ParticlePermutation","GinibrePoincare.continuous_vandermonde_quotient_unique","GinibrePoincare.permutationSign","GinibrePoincare.permute","GinibrePoincare.vandermonde","GinibrePoincare.vandermonde_permute","Group.toDivInvMonoid","HMul.hMul","Int","Int.cast","Int.cast_eq_zero._simp_1","Int.instMonoid","Int.instNontrivial","Int.instSemiring","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","LT.lt","Monoid.toMulOneClass","MonoidHom","MonoidHom.instFunLike","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Ne","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSemiring.toSemigroupWithZero","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoidWithZero","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","True.intro","UniformSpace.toTopologicalSpace","Units","Units.instMulOneClass","Units.ne_zero._simp_1","Units.val","Zero.toOfNat0","congrArg","congrFun","continuous_apply","continuous_pi","eq_false","eq_true","id","instDecidableEqFin","instHMul","instIsDomain","instLTNat","instOfNat","instOfNatNat","mul_assoc","mul_left_cancel\u2080","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EntireVandermondeDivision","name":"GinibrePoincare.continuous_vandermonde_quotient_unique","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Continuous","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","HMul.hMul","LT.lt","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["Complex","Complex.instField","Complex.instMul","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Continuous","DFunLike.coe","ENNReal","ENNReal.instZero","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianMeasure_collisionSet","GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","GinibrePoincare.vandermonde","GinibrePoincare.vandermonde_eq_zero_iff","HMul.hMul","Iff.mp","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.ae_iff","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.EntireVandermondeDivision.0.GinibrePoincare.continuous_vandermonde_quotient_unique._simp_1_1","congrArg","congrFun'","funext","id","instHMul","instIsDomain","instLTNat","instOfNatNat","mul_left_cancel\u2080","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductMollifierLimit","name":"GinibrePoincare.contractions_strong_limit_apply","type_dependencies":["AddCommGroup.toAddCommMonoid","Complex","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Filter.Tendsto","Filter.atTop","LE.le","Nat","Nat.instPreorder","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instOne","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.le_opNorm","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mp","Eq.mpr","Eq.symm","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.add","Filter.atTop","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","Nat","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomIsometric.ids","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_le_add","congr","congrArg","dist_eq_norm","dist_triangle","id","instHAdd","instHMul","instHSub","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","le_refl","map_sub","mul_le_mul_of_nonneg_right","nhds","norm_nonneg","one_mul","squeeze_zero","tendsto_iff_norm_sub_tendsto_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Continuity","name":"GinibrePoincare.contractions_tendsto_on_dense_range","type_dependencies":["AddCommGroup.toAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenseRange","Filter.Tendsto","Filter.atTop","LE.le","Nat","Nat.instPreorder","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigrou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onoid","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.instMembership","Set.mem_univ","Set.univ","Zero.toOfNat0","abs","abs_of_nonneg","add_nonneg","congr","congrArg","convex_Ici","id","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instMulZeroClassOfSemiring","instSMulOfMul","mul_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPotential","name":"GinibrePoincare.convexOn_radial_lift","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","ConvexOn","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Module.toDistribMulAction","MonotoneOn","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instZero","Real.normedField","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul","Set.Ici","Set.univ","SubNegMonoid.toAddMonoid","Zero.toOfNat0","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And.intro","And.right","Convex","ConvexOn","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HAdd.hAdd","HMul.hMul","HSMul.hSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","Membership.mem","Module.toDistribMulAction","MonotoneOn","MulZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instZero","Real.normedField","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.instMembership","Set.univ","SubNegMonoid.toAddMonoid","Zero.toOfNat0","add_nonneg","convexOn_norm","convex_univ","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instMulZeroClassOfSemiring","instSMulOfMul","mul_nonneg","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPotential","name":"GinibrePoincare.convexOn_radial_lift_of_planar","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Complex","Complex.instAddCommMonoid","Complex.instNorm","Complex.instNormedField","Complex.instRCLike","ConvexOn","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","Module.toDistribMulAction","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.normedField","Real.partialOrder","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Set.univ","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","And","And.casesOn","Complex","Complex.instAddCommMonoid","Complex.instNorm","Complex.instNormedField","Complex.instRCLike","ConvexOn","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.convexOn_radial_lift","GinibrePoincare.radial_profile_convex_monotone","Module.toDistribMulAction","MonotoneOn","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instZero","Real.normedField","Real.partialOrder","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Set.Ici","Set.univ","SubNegMonoid.toAddMonoid","Zero.toOfNat0","instSMulOfMul"]},{"kind":"definition","module":"GinibrePoincare.Concrete.Wirtinger","name":"GinibrePoincare.coordinateDirection","type_dependencies":["Complex","Fin","GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instZero","Eq","Fin","Nat","OfNat.ofNat","Zero.toOfNat0","instDecidableEqFin","ite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.coordinateDirection.eq_1","type_dependencies":["Complex","Complex.instZero","Eq","Fin","GinibrePoincare.coordinateDirection","Nat","OfNat.ofNat","Zero.toOfNat0","instDecidableEqFin","ite"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.coordinateDirection","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.coordinateDirection_eq_re_smul_real_add_im_smul_imaginary","type_dependencies":["Algebra.toSMul","Complex","Complex.im","Complex.instAdd","Complex.instNormedField","Complex.instRCLike","Complex.re","Eq","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HSMul.hSMul","Nat","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Pi.instAdd","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instHAdd","instHSMul"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Algebra.toSMul","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.re","Complex.re_add_im","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.ndrec","Eq.symm","Eq.trans","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.instAdd","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","True","Zero.toOfNat0","add_zero","congr","congrArg","dite","eq_false","eq_self","funext","instDecidableEqFin","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","mul_one","of_eq_true","smul_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexProductLSI","name":"GinibrePoincare.coordinateDirectionalEnergy_integrable","type_dependencies":["DecidableEq","EMetricSpace.toPseudoEMetricSpace","Fintype","GinibrePoincare.directionalEnergy","InnerProductSpace.toNormedSpace","LipschitzWith","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MetricSpace.toEMetricSpace","NNReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.single","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instOne","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","pseudoEMetricSpacePi"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWit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riviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.borelSpace","Pi.instPow","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.single","Preorder.toLE","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.log","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","abs","congrArg","congrFun'","deriv","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instClosedIciTopology","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHasSolidNormReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","instTransEq_1","instTransLE","instZeroENat","measurable_fderiv_apply_const","mul_le_mul_of_nonneg_left","mul_one","norm_fderiv_le_of_lipschitz","pseudoEMetricSpacePi","rfl","secondCountableTopologyEither_of_right"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.coordinateMulMultivariateNormalizedL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.coordinateMulMultivariateNormalizedL2._proof_1","GinibrePoincare.memLp_two_coordinate_mul_multivariateNormalized","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp.toLp","Nat","OfNat.ofNat","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.coordinateMulMultivariateNormalizedL2._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.coordinateMulMultivariateNormalizedL2.congr_simp","type_dependencies":["AddCommGroup.toAddGrou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ul.hSMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePhaseCoordinates","name":"GinibrePoincare.coordinatePhaseCLM._proof_1","type_dependencies":["Algebra.toSMul","Complex","Complex.instNormedField","Complex.instRCLike","Distrib.toMul","Field.toSemifield","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","SMulCommClass","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.to_smulCommClass","Complex","Complex.instNormedField","Complex.instRCLike","Field.toSemifield","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePhaseCoordinates","name":"GinibrePoincare.coordinatePhaseCLM._proof_2","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","ContinuousConstSMul","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instSMulOfMul"],"value_dependencies":["Complex","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePhaseCoordinates","name":"GinibrePoincare.coordinatePhaseCLM.eq_1","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","ContinuousLinearMap.proj","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinatePhaseCLM","GinibrePoincare.coordinatePhaseCLM._proof_1","GinibrePoincare.coordinatePhaseCLM._proof_2","HSMul.hSMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinatePhaseCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.mod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inateQuantileTransport_lipschitz","type_dependencies":["CommSemiring.toSemiring","ContDiff","DecidableEq","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","Field.toSemifield","Fintype","GinibrePoincare.coordinateQuantileTransport","InnerProductSpace.toNormedSpace","LE.le","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instLE","Real.instRCLike","Real.lattice","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","abs","deriv","instOneENat","pseudoEMetricSpacePi"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Bool","Bool.false","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.toSeminormedAddCommGroup","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DivisionRing.toRing","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fintype","GinibrePoincare.coordinateQuantileTransport","HMul.hMul","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","LipschitzWith","LipschitzWith.dist_le_mul","LipschitzWith.of_dist_le_mul","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MetricSpace.toEMetricSpace","MetricSpace.toPseudoMetricSpace","MulZeroClass.toMul","NNNorm.nnnorm","NNReal","NNReal.coe_le_coe","NNReal.coe_nonneg","NNReal.instPartialOrder","NNReal.toReal","Nat.cast_one","Nat.cast_zero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","abs","congrArg","deriv","dist_le_pi_dist","dist_nonneg","dist_pi_le_iff","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instHMul","instIsRCLikeNormedField","instMulZeroClassOfSemiring","instOneENat","instZeroENat","lipschitzWith_of_nnnorm_fderiv_le","mul_le_mul_of_nonneg_left","mul_nonneg","norm_deriv_eq_norm_fderiv","pseudoMetricSpacePi"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexProductTransport","name":"GinibrePoincare.coordinateQuantileTransport_measurePreserving","type_dependencies":["DecidableEq","Eq","Fintype","GinibrePoincare.coordinateQuantileTransport","Measurable","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.MeasurePreserving","NNReal","NNReal.instOne","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","Real","Real.instZero","Real.measurableSpace","Zero.toOfNat0"],"value_dependencies":["DecidableEq","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Fintype","Measurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.map","MeasureTheory.MeasurePreserving.mk","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure"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oordinateSum_power_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instSemiring","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreMeasure","HPow.hPow","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Continuous.aestronglyMeasurable","Continuous.pow","ContinuousENorm.toENorm","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_ginibre_gaussian","GinibrePoincare.ginibreMeasure","GinibrePoincare.integrable_norm_pow_complexCoordinateGaussianProbability","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.standardComplexGaussianMeasure","HMul.hMul","HPow.hPow","Iff.mpr","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Measure","MeasureTheory.MeasurePreserving.mk","MeasureTheory.MemLp","MeasureTheory.MemLp.comp_measurePreserving","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.memLp_two_iff_integrable_sq_norm","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.instPow","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.GinibreOneParticleSpectrum.0.GinibrePoincare.coordinateSum_power_memLp._simp_1_1","autoParam","congrArg","congrFun'","continuous_id","funext","id","instCommCStarAlgebraComplex","instHMul","instHPow","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","norm_pow","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOneParticleSpectrum","name":"GinibrePoincare.coordinateSum_power_projectedGradient_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instSemiring","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreMeas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ibrePoincare.Analysis.CorrespondenceBrascampLiebCenter","name":"GinibrePoincare.correspondenceBrascampLiebCenter","type_dependencies":["BorelSpace","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["BorelSpace","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebMean","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instSub","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCenter","name":"GinibrePoincare.correspondenceBrascampLiebCenter.congr_simp","type_dependencies":["BorelSpace","Eq","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCenter","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["BorelSpace","Eq","Eq.rec","Eq.refl","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCenter","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLieb","name":"GinibrePoincare.correspondenceBrascampLiebCenter.eq_1","type_dependencies":["BorelSpace","Eq","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCenter","GinibrePoincare.correspondenceBrascampLiebMean","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instSub","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHSub"],"value_dependencies":["BorelSpace","Eq.refl","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCenter","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCore","name":"GinibrePoincare.correspondenceBrascampLiebCoreL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","CompleteSpace","ContDiff","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","FiniteDimensional","Fintype","GinibrePoincare.CorrespondenceBrascampLiebCompactTest","GinibrePoincare.correspondenceBrascampLiebMeasure","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductS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"Neg.neg","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instStarForall","Pi.instTrivialStarForall","Pi.instZero","Pi.topologicalSpace","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TrivialStar.star_trivial","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","congrArg","congrFun'","dotProduct","dotProduct_zero","eq_self","fderiv","funext","id","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instClosedIciTopology","instCommSemiringENat","instCompleteLinearOrderENat","instDistribOfSemiring","instHMul","instHPow","instHasSolidNormReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instStarRingReal","instTopologicalSpaceMatrix","instTrivialStarReal","measureSpaceOfInnerProductSpace","mul_le_mul_of_nonneg_left","neg_sq","of_eq_true","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakDirichlet","name":"GinibrePoincare.correspondenceBrascampLieb_compact_memLp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","CompleteSpace","Continuous","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebMeasure","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubtractionMonoid","AddMonoidWithOne.toNatCast","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CompleteSpace","Continuous","Continuous.aestronglyMeasurable","Continuous.norm","Continuous.pow","ContinuousENorm.toENorm","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","False","FiniteDimensional","Function.support","GinibrePoincare.correspondenceBrascampLiebMea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iebCompactTest.val","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.correspondenceBrascampLiebCoreL2","GinibrePoincare.correspondenceBrascampLiebCoreL2._proof_2","GinibrePoincare.correspondenceBrascampLiebCoreL2._proof_3","GinibrePoincare.correspondenceBrascampLiebHessian","GinibrePoincare.correspondenceBrascampLiebInverseEnergy","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceBrascampLieb_compact_generator_bound","GinibrePoincare.correspondenceBrascampLieb_toLp_inner","GinibrePoincare.correspondenceBrascampLieb_toLp_norm_sq","HMul.hMul","HPow.hPow","Inner.inner","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","Matrix.PosDef","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Subtype","Top.top","True","True.intro","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.natCast","WithTop.ofNat_ne_top._simp_1","WithTop.one","WithTop.some","WithTop.top","congrArg","eq_false","eq_true","id","instAddMonoidWithOneENat","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instStarRingReal","instTopENat","measureSpaceOfInnerProductSpace","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebDense","name":"GinibrePoincare.correspondenceBrascampLieb_core_orthogonal_constants","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","BorelSpace","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","ContDiff","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toSemifield","FiniteDimensional","Fintype","GinibrePoincare.correspondenceBrascampLiebCoreRange","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceBrascampLiebOneL2","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsFiniteMeasure","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivisionRing","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Set","Set.instSingletonSet","SetLike.instMembership","Singleton.singleton","Submodule","Submodule.orthogonal","Submodule.span","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","BorelSpace","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompleteSpace","CompletelyDistribLattice.toCompleteLattice","ContDiff","ContDiff.comp","ContDiff.neg","ContDiff.of_le","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional","Fintype","Function.hasSMul","GinibrePoincare.CorrespondenceBrascampLiebCompactTest","GinibrePoincare.CorrespondenceBrascampLiebCompactTest.mk","GinibrePoincare.CorrespondenceBrascampLiebCompactTest.val","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLiebCoreL2","GinibrePoincare.correspondenceBrascampLiebCoreRange","GinibrePoincare.correspondenceBrascampLiebCoreRange._proof_1","GinibrePoincare.correspondenceBrascampLiebCoreRange._proof_5","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceBrascampLiebOneL2","GinibrePoincare.correspondenceBrascampLieb_constants_orthogonal","GinibrePoincare.correspondenceBrascampLieb_core_ae","GinibrePoincare.correspondenceBrascampLieb_weighted_generator_eq","GinibrePoincare.correspondenceWeightedEllipticGenerator","GinibrePoincare.correspondenceWeightedEllipticMeasure","GinibrePoincare.correspondenceWeightedElliptic_annihilator_constant","HMul.hMul","HSMul.hSMul","HasCompactSupport","Iff.mpr","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.IsFiniteMeasure","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.memLp_const","Membership.mem","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrthonormalBasis","OrthonormalBasis.instFunLike","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.contDiff_exp","Real.denselyNormedField","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivisionRing","Real.instMul","Real.instNeg","Real.instOne","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.instSingletonSet","Set.ofPred","SetLike.instMembership","Singleton.singleton","SubNegMonoid.toAddMonoid","Submodule","Submodule.instPartialOrder","Submodule.mem_span_singleton","Submodule.orthogonal","Submodule.setLike","Submodule.span","Subtype","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instPreorder","WithTop.instSemiring","WithTop.natCast","WithTop.one","WithTop.some","Zero.toOfNat0","congrArg","congrFun'","conj_trivial","eq_self","fact_one_le_two_ennreal","id","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instDistribOfSemiring","instHMul","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroOneClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPreorderENat","instTopENat","instTrivialStarReal","le_antisymm","measureSpaceOfInnerProductSpace","mul_comm","mul_one","of_eq_true","real_inner_comm","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCutoffs","name":"GinibrePoincare.correspondenceBrascampLieb_cutoff_compact","type_dependencies":["FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCutoff","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Bool","ContDiffBump.hasCompactSupport","ContDiffBump.toFun","DistribMulAction.toMulAction","DivisionSemiring.toGroupWithZero","Eq.refl","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebBump","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HasCompactSupport.comp_homeomorph","Homeomorph.smulOfNeZero","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Module.toDistribMulAction","Monoid.toSemigroup","MonoidWithZero.toMonoid","MulAction.toSemigroupAction","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivisionRing","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0"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ce.toNormedSpace","IsCompact","Membership.mem","Nat","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instOne","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bornology.IsBounded.exists_norm_le","CommRing.toRing","CommSemiring.toSemiring","ContDiffBump.one_of_mem_closedBall","ContDiffBump.rIn","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually","Filter.atTop","Filter.eventually_ge_atTop","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.correspondenceBrascampLiebBump","GinibrePoincare.correspondenceBrascampLiebCutoff","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsCompact","IsCompact.isBounded","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Metric.closedBall","Metric.mem_closedBall","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.ceil","Nat.instCommSemiring","Nat.instPreorder","Nat.le_ceil","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.norm","Real.norm_of_nonneg","Real.normedField","Real.partialOrder","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congrArg","dist_zero_right","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instLENat","instMulZeroClassOfSemiring","instOfNatNat","inv_mul_le_iff\u2080","inv_pos_of_pos","le_of_lt","le_of_not_gt","neg_neg_of_pos","norm_smul","propext","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCutoffs","name":"GinibrePoincare.correspondenceBrascampLieb_cutoff_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebBump","GinibrePoincare.correspondenceBrascampLiebCutoff","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHAdd","instHMul","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.differentiable","ContDiffBump.contDiff","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp_id","ContinuousLinearMap.comp_smul\u209b\u2097","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","ENat","Eq","Eq.mp","Eq.refl","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","Function.comp","GinibrePoincare.correspondenceBrascampLiebBump","GinibrePoincare.correspondenceBrascampLiebCutoff","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.const_smul","HasFDerivAt.fderiv","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsBoundedSMul.toUniformContinuousConstSMul","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instField","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","hasFDerivAt_id","id","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHMul","instHSMul","instIsTopologicalRingReal","instOneENat","instPolynormableSpace","instSMulOfMul","instZeroENat","map_inv\u2080","smulCommClass_self","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCutoffs","name":"GinibrePoincare.correspondenceBrascampLieb_cutoff_smooth","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","ContDiff.comp","ContDiffBump.contDiff","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENat","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebBump","HAdd.hAdd","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instCommMonoid","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","WithTop.some","Zero.toOfNat0","contDiff_const_smul","instHAdd","instHSMul","instTopENat","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCutoffs","name":"GinibrePoincare.correspondenceBrascampLieb_cutoff_unit","type_dependencies":["And","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebCutoff","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Real","Real.instDivisionRing","Real.instLE","Real.instOne","Real.instRCLike","Real.instZero","Real.normedField","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And.intro","ContDiffBump.le_one","ContDiffBump.nonneg","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebBump","GinibrePoincare.correspondenceBrascampLiebCutoff","HAdd.hAdd","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","LE.le","Module.toDistribMulAction","Nat","Nat.cast","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivisionRing","Real.instInv","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebDensityGenerator","name":"GinibrePoincare.correspondenceBrascampLieb_density_derivative","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsWeight","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instMul","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instHMul","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.distribMulAction","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.neg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsWeight","HMul.hMul","HSMul.hSMul","HasDistribNeg.toInvolutiveNeg","HasFDerivAt","HasFDerivAt.exp","HasFDerivAt.fderiv","HasFDerivAt.neg","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LipschitzAdd.continuousAdd","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat.cast_one","Nat.cast_zero","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instNeg","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.hasLipschitzAdd","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instRing","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StrongDual","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instHMul","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOneENat","instPolynormableSpace","instSMulCommClassOfIsScalarTower","instSMulOfMul","instZeroENat","mul_comm","mul_neg","neg_apply","of_eq_true","smul_apply","smul_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebDensityGenerator","name":"GinibrePoincare.correspondenceBrascampLieb_density_generator","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Finset.sum","Finset.univ","Fintype","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","HAdd.hAdd","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instHAdd","instHMul","instOneENat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Finset","Finset.instSetLike","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.univ","Fintype","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLieb_density_derivative","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.Fie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pLiebJets","name":"GinibrePoincare.correspondenceBrascampLieb_direction_commute","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","GinibrePoincare.bakryEmeryGibbsDirectional","InnerProductSpace","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.natCast","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","ContDiff","ContDiff.contDiffAt","ContDiff.differentiable","ContDiff.fderiv_right","ContDiffAt.isSymmSndFDerivAt","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.comp.congr_simp","ContinuousLinearMap.comp_zero","ContinuousLinearMap.flip","ContinuousLinearMap.funLike","ContinuousLinearMap.instAddMonoid","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.topologicalSpace","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.bakryEmeryGibbsDirectional","HAdd.hAdd","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instZero","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Std.le_refl._simp_1","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","True.intro","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instPreorder","WithTop.instSemiring","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","congrFun","congrFun'","differentiableAt_const","eq_self","eq_true","fderiv","fderiv_clm_apply","fderiv_fun_const","funext","id","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCharZeroENat","instCommSemiringENat","instCompleteLinearOrderENat","instHAdd","instIsRCLikeNormedField","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPreorderENat","instReflLe","instZeroENat","minSmoothness","minSmoothness_of_isRCLikeNormedField","of_eq_true","smulCommClass_self","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebJets","name":"GinibrePoincare.correspondenceBrascampLieb_direction_contDiff","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.bakryEmeryGibbsDirectional","HAdd.hAdd","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.add","WithTop.one","instAddENat","instHAdd","instOneENat"],"value_dependencies":["ContDiff","ContDiff.clm_apply","ContDiff.fderiv_right","DenselyNormedField.toNontriviallyNormedField","ENat","HAdd.hAdd","InnerProductSpace","InnerProductSpace.toNormedSpace","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.add","WithTop.instPreorder","WithTop.one","contDiff_const","fderiv","instAddENat","instHAdd","instOneENat","instPreorderENat","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebJets","name":"GinibrePoincare.correspondenceBrascampLieb_direction_mul","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bakryEmeryGibbsDirectional","HAdd.hAdd","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instHAdd","instHMul","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","Algebra.to_smulCommClass","Bool","Bool.false","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.bakryEmeryGibbsDirectional","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","fderiv","fderiv_mul","id","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instMulZeroClassOfSemiring","instOneENat","instSMulOfMul","instZeroENat","rfl","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebLinear","name":"GinibrePoincare.correspondenceBrascampLieb_direction_smul","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Function.hasSMul","GinibrePoincare.bakryEmeryGibbsDirectional","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.one","instHSMul","instOneENat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Function.hasSMul","GinibrePoincare.bakryEmeryGibbsDirectional","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat.cast_one","Nat.cast_zero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","eq_self","fderiv","fderiv_const_smul","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instHMul","instHSMul","instIsTopologicalRingReal","instOneENat","instSMulOfMul","instZeroENat","of_eq_true","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebJets","name":"GinibrePoincare.correspondenceBrascampLieb_direction_sub","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.bakryEmeryGibbsDirectional","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","WithTop","WithTop.one","instHSub","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Bool","Bool.false","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.sub","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivisionRing.toRing","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.bakryEmeryGibbsDirectional","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat.cast_one","Nat.cast_zero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","eq_self","fderiv","fderiv_sub","id","instAddMonoidWithOneENat","instCharZeroENat","instHSub","instOneENat","instZeroENat","of_eq_true","sub_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebDuality","name":"GinibrePoincare.correspondenceBrascampLieb_duality","type_dependencies":["HMul.hMul","HPow.hPow","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","closure","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Continuous.inner","Continuous.mul","Continuous.pow","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Function.swap","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsClosed","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","IsStrictOrderedRing.toMulPosStrictMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tact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roup","AddCommGroup.toDivisionAddCommMonoid","BorelSpace","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Eq","Eq.mp","Eq.trans","Field.toSemifield","FiniteDimensional","Finset","Finset.instSetLike","Finset.sum","Finset.sum_apply","Finset.univ","Fintype","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsGenerator","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.finset_sum","HasCompactSupport.mul_left","HasCompactSupport.sub","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubtractionCommMonoid.toSubtractionMonoid","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fderiv","funext","instHMul","instHSub","instMulZeroClassOfSemiring","measureSpaceOfInnerProductSpace","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCore","name":"GinibrePoincare.correspondenceBrascampLieb_generator_continuous","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","ContDiff","Continuous","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","FiniteDimensional","Fintype","GinibrePoincare.bakryEmeryGibbsGenerator","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CommRing.toNonUnitalCommRing","CompleteSpace","ContDiff","ContDiff.continuous","Continuous.mul","Continuous.sub","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","FiniteDimensional","Finset","Finset.instSetLike","Finset.univ","Fintype","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.correspondenceBrascampLieb_direction_contDiff","HMul.hMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","continuous_finsetSum","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCore","name":"GinibrePoincare.correspondenceBrascampLieb_generator_memLp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","CompleteSpace","ContDiff","ContinuousENorm.toENorm","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","FiniteDimensional","Fintype","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.correspondenceBrascampLiebMeasure","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CompleteSpace","ContDiff","ContDiff.continuous","Continuous","Continuous.aestronglyMeasurable","Continuous.norm","Continuous.pow","ContinuousENorm.toENorm","DecidableEq","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.trans","False","FiniteDimensional","Fintype","Function.support","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceBrascampLieb_generator_compact","GinibrePoincare.correspondenceBrascampLieb_generator_continuous","GinibrePoincare.correspondenceBrascampLieb_integrable_compact","HPow.hPow","HasCompactSupport","HasCompactSupport.mono","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.memLp_two_iff_integrable_sq_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instDivisionRing","Real.instMonoid","Real.instMonoidWithZero","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","congrFun'","eq_self","instHPow","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace","norm_zero","not_false_eq_true","of_eq_true","secondCountableTopologyEither_of_right","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebLinear","name":"GinibrePoincare.correspondenceBrascampLieb_generator_smul","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat",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Group.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","continuous_pi","fderiv","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHAdd","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instZeroENat","measureSpaceOfInnerProductSpace","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebCompactEnergy","name":"GinibrePoincare.correspondenceBrascampLieb_hessian_inverse_continuous","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","ContDiff","Continuous","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","FiniteDimensional","Fintype","GinibrePoincare.correspondenceBrascampLiebHessian","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","Matrix","Matrix.PosDef","Matrix.inv","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopologicalSpaceMatrix","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CommRing.toCommSemiring","CommSemiring.toSemiring","CompleteSpace","ContDiff","Continuous","Continuous.continuousAt","ContinuousAt","ContinuousAt.comp","ContinuousInv\u2080.continuousAt_inv\u2080","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","ENat","ENat.instNatCast","Eq","Eq.mpr","Field.toSemifield","FiniteDimensional","Fintype","GinibrePoincare.correspondenceBrascampLiebHessian","GinibrePoincare.correspondenceBrascampLieb_hessian_continuous","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","Iff.mp","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsTopologicalDivisionRing.toContinuousInv\u2080","IsUnit","IsUnit.ne_zero","Matrix","Matrix.PosDef","Matrix.PosDef.isUnit","Matrix.det","Matrix.inv","Matrix.isUnit_iff_isUnit_det","Matrix.semiring","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instDivisionRing","Real.instField","Real.instMonoidWithZero","Real.instNontrivial","Real.instRCLike","Real.instRing","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Ring.inverse","Ring.inverse_eq_inv'","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","continuousAt_matrix_inv","continuous_iff_continuousAt","id","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopologicalSpaceMatrix","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebGibbs","name":"GinibrePoincare.correspondenceBrascampLieb_integrable_compact","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","Continuous","FiniteDimensional","GinibrePoincare.correspondenceBrascampLiebMeasure","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CompleteSpace","Continuous","Continuous.comp","Continuous.integrable_of_hasCompactSupport","Continuous.mul","Continuous.neg","FiniteDimensional","Function.comp","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceWeightedEllipticMeasure","GinibrePoincare.correspondenceWeightedElliptic_integrable_density","HMul.hMul","HasCompactSupport","HasCompactSupport.mul_left","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toContinuousNeg","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.instMul","Pi.instNeg","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.continuous_exp","Real.exp","Real.exp_pos","Real.instDivisionRing","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebGibbs","name":"GinibrePoincare.correspondenceBrascampLieb_integral_density","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","Continuous","Eq","FiniteDimensional","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLiebMeasure","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","Continuous.comp","Continuous.measurable","Continuous.neg","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","ENNReal.ofReal_lt_top","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mpr","Field.toSemifield","Filter.univ_mem'","FiniteDimensional","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceWeightedEllipticMeasure","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toContinuousNeg","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","Measurable.ennreal_ofReal","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.ae_of_all","MeasureTheory.in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inearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instStarRingReal","instTrivialStarReal","measureSpaceOfInnerProductSpace","mul_le_mul_of_nonneg_left","neg_sq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakDirichlet","name":"GinibrePoincare.correspondenceBrascampLieb_weak_dirichlet","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","CompleteSpace","ContDiff","ContinuousENorm.toENorm","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","FiniteDimensional","Fintype","GinibrePoincare.CorrespondenceBrascampLiebHasWeakGradient","GinibrePoincare.CorrespondenceBrascampLiebLocallyL2","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.correspondenceBrascampLiebGradient","GinibrePoincare.correspondenceBrascampLiebMeasure","HMul.hMul","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instDivisionRing","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","dotProduct","instHMul","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","BorelSpace","BorelSpace.opensMeasurable","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompleteSpace","CompletelyDistribLattice.toCompleteLattice","ContDiff","ContDiff.continuous","ContDiff.of_le","Continuous","Continuous.comp","Continuous.mul","Continuous.neg","Continuous.sub","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.HolderConjugate.instTwoTwo","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FiniteDimensional","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.sum_neg_distrib","Finset.univ","Fintype","Function.comp","GinibrePoincare.CorrespondenceBrascampLiebHasWeakGradient","GinibrePoincare.CorrespondenceBrascampLiebLocallyL2","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLiebGradient","GinibrePoincare.correspondenceBrascampLiebMeasure","GinibrePoincare.correspondenceBrascampLieb_compact_memLp","GinibrePoincare.correspondenceBrascampLieb_direction_contDiff","GinibrePoincare.correspondenceBrascampLieb_localL2_locallyIntegrable","GinibrePoincare.correspondenceBrascampLieb_weak_weighted_adjoint","GinibrePoincare.correspondenceWeightedEllipticMeasure","GinibrePoincare.correspondenceWeightedElliptic_integrable_density","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","HasCompactSupport.sub","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat"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nUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","fderiv_mul","id","inferInstance","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSMulOfMul","instTransEq","instZeroENat","measureSpaceOfInnerProductSpace","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceBrascampLiebDense","name":"GinibrePoincare.correspondenceBrascampLieb_weighted_generator_eq","type_dependencies":["AddCommGroup.toAddGroup","BorelSpace","CompleteSpace","ContDiff","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","FiniteDimensional","Fintype","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceWeightedEllipticGenerator","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrthonormalBasis","OrthonormalBasis.instFunLike","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","BorelSpace","CommSemiring.toSemiring","CompleteSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.mpr","Field.toSemifield","FiniteDimensional","Finset.sum","Finset.sum_add_distrib","Finset.univ","Fintype","GinibrePoincare.bakryEmeryGibbsDirectional","GinibrePoincare.bakryEmeryGibbsGenerator","GinibrePoincare.bakryEmeryGibbsWeight","GinibrePoincare.correspondenceBrascampLieb_density_generator","GinibrePoincare.correspondenceWeightedEllipticGenerator","HAdd.hAdd","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","MeasurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrthonormalBasis","OrthonormalBasis.instFunLike","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivisionRing","Real.instInv","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","congrArg","fderiv","funext","id","instHAdd","instHMul","instOneENat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsAlmostSureStopping","name":"GinibrePoincare.correspondenceBrownian_ae_finite_stopping","type_dependencies":["Exists","Filter.Eventually","Fin","GinibrePoincare.ginibreBrownianAugmentedFiltration","LE.le","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.IsStoppingTime","MeasureTheory.IsStoppingTime.measurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","NNReal","NNReal.instPartialOrder","NNReal.instZero","Nat","Ne","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","Prod","Real","Top.top","WithTop","WithTop.some","WithTop.top","WithTop.untopD","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["And","And.intro","And.left","And.right","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","Conditional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iring","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","Top.top","TopologicalSpace.pseudoMetrizableSpace_pi","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceCollisionRates.0.GinibrePoincare.compact_tube_integral_bound","abs","abs_zero","addRightReflectLE_of_addLeftReflectLE","and_true","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","continuous_const","contravariant_lt_of_covariant_le","div_one","eq_self","fact_one_le_two_ennreal","ge_iff_le._simp_1","id","inferInstance","instAddNat","instCountableFin","instDecidableEqNat","instDecidableNot","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsCancelMulZero","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTFin","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instSigmaCompactSpaceForallOfFinite","instTopENat","le_of_lt","le_of_not_gt","locallyCompact_of_proper","mul_le_mul_of_nonneg_left","mul_nonneg","mul_nonneg_of_nonpos_of_nonpos","mul_one","mul_pos","norm_zero","not_false_eq_true","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","pow_nonneg","pow_pos","rfl","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable","sq_abs","sq_nonneg","sub_self","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCollisionCutoff","name":"GinibrePoincare.correspondenceCollisionCutoff_gradient","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instSemiring","Complex.instSub","Complex.normSq","ContDiffBump.toFun","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Fin","FiniteDimensional.rclike_to_real","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.correspondenceCollisionCutoff","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.sobolevCutoffBump","HDiv.hDiv","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Neg.neg","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithLp.instSMul","Zero.toOfNat0","deriv","instHDiv","instHPow","instHSMul","instHSub","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommGroupWithZero.toDivisionCommMonoid","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instSub","Complex.normSq","ContDiff","ContDiff.differentiable","ContDiffBump.contDiff","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.sub","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasDerivAt","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMono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_proof_7","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootForm","name":"GinibrePoincare.correspondenceComplexFormResolvent._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.correspondenceComplexFormResolvent._proof_7","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootForm","name":"GinibrePoincare.correspondenceComplexFormResolvent_adjoint","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.adjoint","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Field.toCommRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.CorrespondenceComplexFormSpace","GinibrePoincare.CorrespondenceComplexFormSpace._proof_1","GinibrePoincare.CorrespondenceComplexFormSpace._proof_2","GinibrePoincare.CorrespondenceComplexFormSpace._proof_3","GinibrePoincare.CorrespondenceComplexFormSpace._proof_4","GinibrePoincare.CorrespondenceComplexFormSpace._proof_6","GinibrePoincare.CorrespondenceComplexFormSpace._proof_7","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceComplexFormResolvent","GinibrePoincare.correspondenceComplexFormValue","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormSpace_complete","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.ins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":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootForm","name":"GinibrePoincare.correspondenceComplexFormValue_im","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.CorrespondenceComplexFormSpace","GinibrePoincare.CorrespondenceComplexFormSpace._proof_1","GinibrePoincare.CorrespondenceComplexFormSpace._proof_2","GinibrePoincare.CorrespondenceComplexFormSpace._proof_3","GinibrePoincare.CorrespondenceComplexFormSpace._proof_4","GinibrePoincare.CorrespondenceComplexFormSpace._proof_6","GinibrePoincare.CorrespondenceComplexFormSpace._proof_7","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceComplexFormValue","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormValue","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","WithLp.snd","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","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LinearMap.instStarRingId","ContinuousLinearMap.module","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStarNormal","IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instSMulCommClass","Membership.mem","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toIsScalarTower","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCStarAlgebra.toSMulCommClass","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toMetricSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toNonUnitalRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootCalculus","name":"GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_28","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Real","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","Real","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootCalculus","name":"GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_29","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","RCLike.toDenselyNormedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","DenselyNormedField.toNormedField","InnerProductSpace.toNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","NormedAddCommGroup.toSeminormedAddCommGroup","RCLike.innerProductSpace","RCLike.toDenselyNormedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootCalculus","name":"GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_3","type_dependencies":["AddCommGroup.toAddGroup","CommCStarAlgebra.toNormedCommRing","Complex","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootCalculus","name":"GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_30","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_1","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_10","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_28","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_29","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_9","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulCommClass","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSem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iring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CFC.sqrt","CFC.sqrt_nonneg","CStarAlgebra.toNonUnitalCStarAlgebra","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNontrivial","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.algebra","ContinuousLinearMap.applyModule","ContinuousLinearMap.applySMulCommClass","ContinuousLinearMap.continuousConstSMul_apply","ContinuousLinearMap.instLoewnerPartialOrder","ContinuousLinearMap.instNonnegSpectrumClassRealId","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.instStarOrderedRing","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.isScalarTower","ContinuousLinearMap.module","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.semiring","ContinuousLinearMap.smulCommClass","ContinuousLinearMap.sub","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceFriedrichsComplementSqrt","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_1","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_2","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_4","GinibrePoincare.correspondenceFriedrichsComplementSqrt._proof_5","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreMeasure","HSub.hSub","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStarNormal","IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","LE.le.isSelfAdjoint","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Lp.instSMulCommClass","Membership.mem","MetricSpace.toPseudoMetricSpace","Module.complexToReal","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NegZeroClass.toZero","NonUnitalCStarAlgebra.toIsScalarTower","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCStarAlgebra.toSMulCommClass","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedComm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.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNonUnitalCStarAlgebra","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNontrivial","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.module","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStarNormal","IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instSMulCommClass","Membership.mem","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toIsScalarTower","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCStarAlgebra.toSMulCommClass","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toMetricSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toNonUnitalRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","name":"GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_28","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedComm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inibrePoincare.correspondenceFriedrichsResolventSqrt._proof_29","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_9","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulCommClass","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsScalarTower.to_smulCommClass'","MeasurableSpace.pi","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Lp.instSMulCommClass","Module.complexToReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instRCLike","Real.normedCommRing","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","name":"GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_31","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_1","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_10","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_28","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_29","GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_9","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCo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ne.toNatCast","Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.Lp.instCompleteSpace","Nat","OfNat.ofNat","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","name":"GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","name":"GinibrePoincare.correspondenceFriedrichsResolventSqrt._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.instNormedAddCommGroup","ContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup.toContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","name":"GinibrePoincare.correspondenceFriedrichsResolventSqrt.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceFriedrichsResolventSqrt","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRi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L2._proof_1","GinibrePoincare.correspondenceFriedrichsComplementSqrt","GinibrePoincare.correspondenceFriedrichsResolventSqrt","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNonUnitalCStarAlgebra","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Commute","Commute.cfc\u2099_nnreal","Commute.one_right","Commute.refl","Commute.sub_right","Commute.symm","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNontrivial","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.algebra","ContinuousLinearMap.applyModule","ContinuousLinearMap.applySMulCommClass","ContinuousLinearMap.continuousConstSMul_apply","ContinuousLinearMap.instLoewnerPartialOrder","ContinuousLinearMap.instMul","ContinuousLinearMap.instNonnegSpectrumClassRealId","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarOrderedRing","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.instT2Space","ContinuousLinearMap.isScalarTower","ContinuousLinearMap.module","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.semiring","ContinuousLinearMap.smulCommClass","ContinuousLinearMap.sub","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreMeasure","HSub.hSub","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStarNormal","IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopological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reSpatialCutoff","GinibrePoincare.ginibreSpatialCutoff_smooth","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreCutoff","name":"GinibrePoincare.correspondenceNumberCutoff._proof_2","type_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.ofReal","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ginibreSpatialCutoff","HMul.hMul","HasCompactSupport","MulZeroClass.toMul","MulZeroClass.toZero","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.instMul","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.ofReal_zero","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ginibreSpatialCutoff","GinibrePoincare.ginibreSpatialCutoff_compact","HasCompactSupport.comp_left","HasCompactSupport.mul_right","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instMulZeroClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreCutoff","name":"GinibrePoincare.correspondenceNumberCutoff.congr_simp","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.ndrec","Fin","Fin.fintype","GinibrePoincare.BKCompactTest","GinibrePoincare.Configuration","GinibrePoincare.correspondenceNumberCutoff","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.ndrec","Eq.rec","Eq.refl","Fin","Fin.fintype","GinibrePoincare.BKCompactTest","GinibrePoincare.Configuration","GinibrePoincare.correspondenceNumberCutoff","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreCutoff","name":"GinibrePoincare.correspondenceNumberCutoff.eq_1","type_dependencies":["Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.ofReal","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.BKCompactTest","GinibrePoincare.BKCompactTest.mk","GinibrePoincare.Configuration","GinibrePoincare.correspondenceNumberCutoff","GinibrePoincare.correspondenceNumberCutoff._proof_1","GinibrePoincare.correspondenceNumberCutoff._proof_2","GinibrePoincare.ginibreSpatialCutoff","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNo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rmite_polynomial","type_dependencies":["Complex","Eq","Exists","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedPolynomialEval","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.addCommGroup","AddMonoidAlgebra.commRing","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toNatCast","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.ofReal","Complex.ofReal_mul","DFunLike.coe","Distrib.toMul","Eq","Eq.refl","Eq.trans","Exists.intro","Fin","Fin.fintype","Fin.instCommMonoid","Fin.instNeZeroHAddNatOfNat_mathlib_1","Fin.instNonUnitalCommRing","Fin.instOfNat","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","Finsupp","Finsupp.instAdd","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.normalizedEval_eq_sum","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedPolynomialEval","GinibrePoincare.ginibreMixedPolynomialEval._proof_1","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","LT.lt","Membership.mem","Min.min","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.C_mul","MvPolynomial.C_neg","MvPolynomial.C_pow","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.factorial","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalRingHomClass.toMulHomClass","OfNat.ofNat","Prod","Prod.fst","Prod.mk","Prod.snd","Real","Real.instMul","Real.instNatCast","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","congr","congrArg","congrFun'","eq_self","funext","instAddNat","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLTNat","instMinNat","instOfNatNat","instSubNat","ite","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","map_mul","map_natCast","map_neg","map_pow","map_prod","map_sum","of_eq_true","one_ne_zero._simp_1","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreJets","name":"GinibrePoincare.correspondenceNumber_secondCutoff_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.sobolevCutoff","HMul.hMul","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddC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Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolvent._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_2","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_4","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_5","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap.continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolvent.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing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ComplexResolventReal._proof_5","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_6","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_7","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_8","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_9","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_10","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_11","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_12","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","D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normedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_3","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","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Monoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.CorrespondenceOperatorComplex.0.GinibrePoincare.correspondenceOperatorComplexResolventReal_I._abel_1_2","add_apply","congr","congrArg","congrFun'","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","map_neg","neg_one_smul","smul_add","smul_apply","smul_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorConservation","name":"GinibrePoincare.correspondenceOperatorComplexResolvent_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL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inibreFullComplexIm","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplex_decomposition","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","Iff.intro","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","map_zero","of_eq_true","smul_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFixedSpace","name":"GinibrePoincare.correspondenceOperatorComplexResolvent_fixed_iff_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","Iff","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSM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Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolvent_im","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.comp","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorComplexResolventReal","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_10","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_11","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_12","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_15","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_16","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_2","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_4","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_5","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_6","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_7","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_8","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_9","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexIm_I","GinibrePoincare.ginibreFullComplexIm_ofReal","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ofReal","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SemilinearMapClass.toAddHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","map_add","of_eq_true","smul_apply","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplexResolvent_injective","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Function.Injective","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Measu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ansition._proof_11","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedField","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorStochasticSemigroup","name":"GinibrePoincare.correspondenceOperatorComplexStochasticTransition._proof_2","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorStochasticSemigroup","name":"GinibrePoincare.correspondenceOperatorComplexStochasticTransition._proof_3","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorStochasticSemigroup","name":"GinibrePoincare.correspondenceOperatorComplexStochasticTransition._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.correspondenceOperatorComplexStochasticTransition._proof_2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFu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","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorStochasticSemigroup","name":"GinibrePoincare.correspondenceOperatorComplexStochasticTransition._proof_9","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorComplex","name":"GinibrePoincare.correspondenceOperatorComplex_scalar_decomposition","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.re","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","Complex.re","Complex.re_add_im","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Module.complexToReal","Module.toDistribMulAction","MulAction.toSemigroupAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semigroup.toMul","SemigroupAction.mul_smul","SemigroupAction.toSMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","add_smul","congrArg","eq_self","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorSemigroupComparison","name":"GinibrePoincare.correspondenceOperatorContractionSemigroup_eq_from_actual_laplace","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMu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ommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorEvolution._proof_1","GinibrePoincare.correspondenceOperatorEvolution._proof_2","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventCfcEvolution","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CompleteSpace","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.Lp.instCompleteSpace","Nat","OfNat.ofNat","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution_add","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.instMul","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instSemiring","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorEvolution._proof_1","GinibrePoincare.correspondenceOperatorEvolution._proof_2","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventCfcEvolution_add","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorConservation","name":"GinibrePoincare.correspondenceOperatorEvolution_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologi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stOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Continuous.continuousOn","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.ring","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorCfc_im_zero","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_continuous","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instSMulCommClass","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.toReal","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution_isPositive","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ContinuousLinearMap.IsPositive","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincar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","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorComplexResolvent_spectrum","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventCfcEvolution_norm_le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution_ofReal","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass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ibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.ginibreMeasure","IsSelfAdjoint","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorEvolution._proof_1","GinibrePoincare.correspondenceOperatorEvolution._proof_2","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventCfcEvolution_selfAdjoint","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","name":"GinibrePoincare.correspondenceOperatorEvolution_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.one","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instZero","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Normed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","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSecondBounds","name":"GinibrePoincare.correspondenceOperatorFiniteSecond._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSecondBounds","name":"GinibrePoincare.correspondenceOperatorFiniteSecond._proof_7","type_dependencies":["Complex","Complex.instSemiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Complex","Complex.instSemiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberBochnerClosure","name":"GinibrePoincare.correspondenceOperatorFiniteSecond.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.module","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorFiniteSecond","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup"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o.toOfNat0","congrArg","fact_one_le_two_ennreal","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","mul_nonneg","neg_eq_zero","norm_nonneg","rfl","sq_le_sq\u2080","sq_nonneg","sub_eq_zero_of_eq"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormCoordinates","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.prod","DistribMulAction.toDistribSMul","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormCoordinates._proof_1","GinibrePoincare.correspondenceOperatorFormCoordinates._proof_4","GinibrePoincare.correspondenceOperatorFormCoordinates._proof_5","GinibrePoincare.correspondenceOperatorWeakSpace._proof_10","GinibrePoincare.correspondenceOperatorWeakSpace._proof_11","GinibrePoincare.correspondenceOperatorWeakSpace._proof_3","GinibrePoincare.correspondenceOperatorWeakSpace._proof_4","GinibrePoincare.correspondenceOperatorWeakSpace._proof_7","GinibrePoincare.correspondenceOperatorWeakSpace._proof_9","GinibrePoincare.ginibreMeasure","HSMul.hSMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","NormedAddCommGroup.toAddCo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ratorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_1","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instRCLike","RingHomInvPair","Semifield.toCommSemiring","starRingEnd"],"value_dependencies":["DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instRCLike","RingHomInvPair.instStarRingEnd","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_2","type_dependencies":["DenselyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","Ring.toSemiring","RingHom.id","RingHomIsometric","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toNonAssocSemiring"],"value_dependencies":["DenselyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHomIsometric.ids","SeminormedCommRing.toSeminormedRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_3","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","SMulCommClass","Semifield.toCommSemiring","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_4","type_dependencies":["CommSemiring.toSemiring","ContinuousConstSMul","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instDistribOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","ContinuousAdd","DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["ContinuousLinearMap.addCommGroup._proof_7","DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_6","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_7","type_dependencies":["AddCommGroup.toAddGroup","DenselyNormedField.toNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent._proof_8","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","DenselyNormedField.toNormedField","Distrib.toAdd","Field.toCommRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","DenselyNormedField.toNormedField","Field.toCommRing","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolventCLM","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup",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ibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolventLinear","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instMul","Real.instOne","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdSeminormedAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormResolventLinear","GinibrePoincare.correspondenceOperatorFormResolvent_norm_le","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real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CommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolventLinear","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorFormResolvent_norm_le","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheo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mmGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioo","Set.instMembership","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorGenerator_real_difference_dissipative","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.realHilbert_orbit_unique_of_dissipative_derivative","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioo","Set.instMembership","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorOrbits","name":"GinibrePoincare.correspondenceOperatorGenerator_real_scaled_orbit_unique","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","HSMul.hSMul","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureThe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espondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorGenerator_resolvent_exists","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","Membership.mem","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","EuclideanSpace","Exists","Exists.intro","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.correspondenceOperatorFormGradient","GinibrePoincare.correspondenceOperatorFormOfWeak","GinibrePoincare.correspondenceOperatorFormOfWeak_gradient","GinibrePoincare.correspondenceOperatorFormOfWeak_value","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormResolvent_riesz","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormSpace_inner","GinibrePoincare.correspondenceOperatorFormSpace_weak","GinibrePoincare.correspondenceOperatorFormValue","GinibrePoincare.correspondenceOperatorWeakSpace","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatC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roup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorGenerator","GinibrePoincare.ginibreMeasure","IsSelfAdjoint","LT.lt","LinearPMap","LinearPMap.instStar","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent","GinibrePoincare.correspondenceOperatorComplexResolventReal._proof_1","GinibrePoincare.correspondenceOperatorComplexResolvent_denseRange","GinibrePoincare.correspondenceOperatorComplexResolvent_injective","GinibrePoincare.correspondenceOperatorComplexResolvent_isSelfAdjoint","GinibrePoincare.ginibreMeasure","GinibrePoincare.resolventGenerator_selfAdjoint","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorSmoothIdentification","name":"GinibrePoincare.correspondenceOperatorGenerator_smooth_graph","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.correspondenceOperatorGenerator","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid"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SubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.instOne","Real.lattice","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","abs","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","Complex","Complex.instNormedAddCommGroup","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorHermiteMultiplier._proof_1","GinibrePoincare.correspondenceOperatorHermiteMultiplier._proof_2","GinibrePoincare.correspondenceOperatorHermiteMultiplier._proof_3","GinibrePoincare.correspondenceOperatorHermiteMultiplier._proof_4","GinibrePoincare.correspondenceOperatorHermiteMultiplierCoefficients._proof_2","GinibrePoincare.correspondenceOperatorHermiteMultiplierCoefficients._proof_3","GinibrePoincare.correspondenceOperatorHermiteMultiplierValue","LE.le","LT.lt","LinearMap.mk","LinearMap.mkContinuous","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.instOne","Real.lattice","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","abs","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorHermiteMultiplier","name":"GinibrePoincare.correspondenceOperatorHermiteMultiplier._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorHermiteMultiplierVa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respondenceOperatorHermiteMultiplierCoefficients._proof_3","GinibrePoincare.correspondenceOperatorHermiteMultiplierValue._proof_1","GinibrePoincare.correspondenceOperatorHermiteMultiplierValue._proof_2","GinibrePoincare.gaussianHermiteHilbertBasis","HilbertBasis.repr","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PreLp","PreLp.instAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instAddGroup","Real.instLE","Real.instOne","Real.lattice","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","abs","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","lp","lp.instModuleSubtypePreLpMemAddSubgroup","lp.normedAddCommGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorHermiteMultiplier","name":"GinibrePoincare.correspondenceOperatorHermiteMultiplierValue._proof_1","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RingHom.id","RingHomInvPair","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RingHomInvPair.ids","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorHermiteMultiplier","name":"GinibrePoincare.correspondenceOperatorHermiteMultiplierValue._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.ComplexHermite.HermiteMultiIndex","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","RCLike.toDenselyNormedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instRCLike","DenselyNormedField.toNormedField","GinibrePoincare.ComplexHermite.HermiteMultiIndex","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","RCLike.toDenselyNormedField","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorHermiteMultiplier","name":"GinibrePoincare.correspondenceOperatorHermiteMultiplierValue.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorHermiteMultiplierValue","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.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Space","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","forall_congr","funext","implies_true","inner_zero_right","instHMul","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberDomain","name":"GinibrePoincare.correspondenceOperatorNumberGraph._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instHSMul","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.multivariateNormalizedL2","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UnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberDomain","name":"GinibrePoincare.correspondenceOperatorNumberGraph._proof_7","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberDomain","name":"GinibrePoincare.correspondenceOperatorNumberGraph._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberGraph._proof_4","GinibrePoincare.correspondenceOperatorNumberGraph._proof_7","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberDomain","name":"GinibrePoincare.correspondenceOperatorNumberGraph._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.Co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inormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_5","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_6","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_7","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_4","GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_7","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralSelfAdjoint","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph_adjoint","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralGraph","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instLE","Real.instZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Submodule","Submodule.adjoint","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCancelMonoid.toAddRightCancelMonoid","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddRightCancelMonoid.toAddRightCancelSemigroup","AddRightCancelSemigroup.toIsRightCancelAdd","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.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umberSpectralGraph","name":"GinibrePoincare.correspondenceOperatorNumberSpectralGraph_singleValued","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralGraph","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DenselyNormedField.toNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralGraph","GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_4","GinibrePoincare.correspondenceOperatorNumberSpectralGraph._proof_5","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient.congr_simp","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.gaussianHermiteCoefficient_ext","GinibrePoincare.multivariateNormalizedL2","HMul.hMul","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_mul","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSe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AddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.range","Set.univ","SetLike.coe","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.bot_orthogonal_eq_top","Submodule.instBot","Submodule.instTop","Submodule.orthogonal","Submodule.setLike","Submodule.topologicalClosure","Submodule.topologicalClosure_coe","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","closure","congrArg","dense_iff_closure_eq","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","propext","smulCommClass_self","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralResolvent","name":"GinibrePoincare.correspondenceOperatorNumberSpectralResolvent_injective","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Function.Injective","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralResolvent","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Bool","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_add._simp_1","Complex.ofReal_inj._simp_1","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralResolvent","GinibrePoincare.correspondenceOperatorNumberSpectralResolvent_coefficient","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_ext","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HMul.hMul","Inv.inv","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_pos_of_pos_of_nonneg","cast","congr","congrArg","congrFun'","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHMul","instIsDomain","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","inv_ne_zero","mul_left_cancel\u2080","ne_of_gt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralResolvent","name":"GinibrePoincare.correspondenceOperatorNumberSpectralResolvent_isSelfAdjoint","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.instStarId","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectralResolvent","IsSelfAdjoint","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring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oid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","cfc","congrArg","congrFun'","fact_one_le_two_ennreal","id","inner_smul_left","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instStarRingReal","smulCommClass_self","spectrum","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactGraph","name":"GinibrePoincare.correspondenceOperatorNumber_compact_graph","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.BKCompactTest","GinibrePoincare.BKCompactTest.l2","GinibrePoincare.Configuration","GinibrePoincare.bkCompactNumberL2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumber","InnerProductSpace.toNormedSpace","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","And","And.intro","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","ContDiff.of_le","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Exists","Exists.intro","False","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.BKCompactTest","GinibrePoincare.BKCompactTest.adjoint","GinibrePoincare.BKCompactTest.compact","GinibrePoincare.BKCompactTest.dbar","GinibrePoincare.BKCompactTest.l2","GinibrePoincare.BKCompactTest.l2_coe","GinibrePoincare.BKCompactTest.smooth","GinibrePoincare.BKCompactTest.toFun","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.IsGaussianWeakDbar._proof_1","GinibrePoincare.bkCompactNumberL2","GinibrePoincare.bkCompactNumberL2._proof_1","GinibrePoincare.bkCompactNumberL2._proof_2","GinibrePoincare.bkCompactNumberL2._proof_3","GinibrePoincare.bkCompactNumberL2._proof_5","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumber","GinibrePoincare.correspondenceOperatorNumber_graph_iff_ordinary_form","GinibrePoincare.gaussianDbarAdjointTest","GinibrePoincare.gaussianDbarAdjointTestL2","GinibrePoincare.gaussianDbarAdjointTestL2._proof_1","GinibrePoincare.gaussianDbarAdjointTest_memLp","GinibrePoincare.gaussian_smooth_weak_dbar","GinibrePoincare.smoothCompactL2","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ex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ibrePoincare.correspondenceNumberCompactSmoothGraph._proof_1","GinibrePoincare.correspondenceOperatorNumber","GinibrePoincare.correspondenceOperatorNumberGraph","GinibrePoincare.correspondenceOperatorNumberGraph_isClosed","GinibrePoincare.correspondenceOperatorNumber_compact_graph","GinibrePoincare.correspondenceOperatorNumber_finite_compact_core","GinibrePoincare.correspondenceOperatorNumber_finite_core","GinibrePoincare.correspondenceOperatorNumber_graph","GinibrePoincare.finiteGaussianNumberL2","GinibrePoincare.gaussianHermiteFiniteCoefficients","InnerProductSpace.toNormedSpace","IsClosed","IsClosed.mem_of_tendsto","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.casesOn","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Subset.antisymm","Set.instMembership","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","closure","closure_minimal","congrArg","fact_one_le_two_ennreal","id","instLTNat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","isClosed_closure","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberTransfer","name":"GinibrePoincare.correspondenceOperatorNumber_complement_weak","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.zero","And","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","HAdd.hAdd","HPow.hPow","HSub.hSub","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instMonoid","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.zero","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","DenselyNormedField.toNormedField","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mem_univ","Finset.single_le_sum","Finset.sum","Finset.sum_congr","Finset.univ","Function.update","Function.update_self","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.gaussianHermiteCoefficient_ext","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianWeakDbar_hermit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roup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","fact_one_le_two_ennreal","id","inferInstance","instDecidableEqNat","instDecidableNot","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","mul_comm","mul_le_mul_of_nonneg_left","mul_nonneg","mul_one","neg_eq_zero","norm_nonneg","norm_zero","of_decide_eq_true","one_mul","rfl","sq_le_sq\u2080","sq_nonneg","sub_eq_zero_of_eq","sub_zero","zero_lt_one","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberTransfer","name":"GinibrePoincare.correspondenceOperatorNumber_ginibre_shifted_root_deficit","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","And","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectral","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.ginibreFullCenteredTransform","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.normedAddCommGroup","Real.sqrt","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Bool","Bool.false","Bool.true","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.in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Nat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberForm","name":"GinibrePoincare.correspondenceOperatorNumber_graph_iff_ordinary_form","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumber","Iff","Inner.inner","InnerProductSpace.toNormedSpace","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toModule","And","And.casesOn","And.intro","Classical.choose","Classical.choose_spec","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.conj_natCast","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Finsupp","Finsupp.distribMulAction","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instZero","Finsupp.linearCombination","Finsupp.linearCombination_single","Finsupp.module","Finsupp.single","Finsupp.smulZeroClass","Finsupp.smul_single","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_1","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_2","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_3","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_5","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_6","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_2","GinibrePoincare.ComplexHermite.memLp_two_multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumber","GinibrePoincare.correspondenceOperatorNumberGraph","GinibrePoincare.correspondenceOperatorNumberGraph._proof_4","GinibrePoincare.correspondenceOperatorNumberGraph._proof_5","GinibrePoincare.correspondenceOperatorNumber_finite_form","GinibrePoincare.correspondenceOperatorNumber_form_identity","GinibrePoincare.correspondenceOperatorNumber_graph","GinibrePoincare.correspondenceOperatorNumber_weak_dbar_exists","GinibrePoincare.finiteDbarComponentL2","GinibrePoincare.finiteGaussianNumberL2","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.gaussian_finiteHermite_weak_dbar","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.multivariateNormalizedL2._proof_1","GinibrePoincare.spectralNumberCoefficients","HMul.hMul","HSMul.hSMul","Iff.intro","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp.toLp","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NNRat","Nat","Nat.cast","Nat.cast_mul","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","RingHomClass.toNonUnitalRingHomClass","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.setLike","Subtype","True","UniformSpace.toTopologicalSpace","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","funext","id","inner_conj_symm","inner_smul_right","instCommSemiringNNRat","instDistribOfSemiring","instHMul","instHSMul","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","map_mul","map_sum","mul_one","of_eq_true","one_smul","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberResolvent","name":"GinibrePoincare.correspondenceOperatorNumber_graph_iff_resolvent","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperato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torNumberSquareRoot","name":"GinibrePoincare.correspondenceOperatorNumber_shifted_sqrt_exists","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectral","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instNatCast","Real.instSub","Real.sqrt","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.measurableSpace","Complex.norm_real","Complex.ofReal","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","False","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperatorNumberSpectral","GinibrePoincare.correspondenceOperatorNumberSpectral_domain_iff","GinibrePoincare.correspondenceOperatorNumber_ordinary_form_hasSum","GinibrePoincare.gaussianHermiteCoefficient","HMul.hMul","HPow.hPow","HSub.hSub","HasSum.summable","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_mul","Nat.cast_nonneg","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.decidableLE","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.partialOrder","Real.pseudoMetri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onRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap.IsScalarTower.compatibleSMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","name":"GinibrePoincare.correspondenceOperatorRealEvolution._proof_2","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","name":"GinibrePoincare.correspondenceOperatorRealEvolution._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.correspondenceOperatorRealEvolution._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","name":"GinibrePoincare.correspondenceOperatorRealEvolution._proof_4","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGr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emiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","name":"GinibrePoincare.correspondenceOperatorRealEvolution._proof_9","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorSemigroupComparison","name":"GinibrePoincare.correspondenceOperatorRealEvolution.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorMarkov","name":"GinibrePoincare.correspondenceOperatorRealEvolution_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.correspondenceOperatorEvolution_constant","GinibrePoincare.correspondenceOperatorEvolution_ofReal","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexOfReal_ae","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ofReal","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullConstant_ae","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","GinibrePoincare.ginibreRealConstantL2_ae","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congr","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorSemigroupComparison","name":"GinibrePoincare.correspondenceOperatorRealEvolution_continuous_orbit","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instTopologicalSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousLinearMap.restrictScalars","ContinuousLinearMap.toLinearMap","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.continuous_correspondenceOperatorEvolution","GinibrePoincare.correspondenceOperatorEvolution","GinibrePoincare.correspondenceOperatorRealEvolution._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution._proof_10","GinibrePoincare.correspondenceOperatorRealEvolution._proof_11","GinibrePoincare.correspondenceOperatorRealEvolution._proof_2","GinibrePoincare.correspondenceOperatorRealEvolution._proof_3","GinibrePoincare.correspondenceOperatorRealEvolution._proof_4","GinibrePoincare.correspondenceOperatorRealEvolution._proof_5","GinibrePoincare.correspondenceOperatorRealEvolution._proof_7","GinibrePoincare.correspondenceOperatorRealEvolution._proof_8","GinibrePoincare.correspondenceOperatorRealEvolution._proof_9","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instTopologicalSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorRealErgodicity","name":"GinibrePoincare.correspondenceOperatorRealEvolution_ergodic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.integral","Membership.mem","NNReal","NNReal.instPartialOrder","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing",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measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.refl","Field.toDivisionRing","Field.toSemifield","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.correspondenceOperatorRealEvolution.congr_simp","GinibrePoincare.correspondenceOperatorRealEvolution_graph_derivative","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","HMul.hMul","HSMul.hSMul","HSub.hSub","HasDerivAt","HasDerivAt.congr_simp","HasDerivAt.const_mul","HasDerivAt.scomp","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_coe","Real.toNNReal_mul","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","hasDerivAt_id","id","instDistribOfSemiring","instHMul","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","mul_one","mul_pos"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorSemigroupComparison","name":"GinibrePoincare.correspondenceOperatorRealEvolution_zero_apply","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorRealEvolution","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Me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isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorValueResolvent.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorConservation","name":"GinibrePoincare.correspondenceOperatorValueResolvent_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRi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.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","inner_zero_left","instFintypeProd","instHAdd","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","of_eq_true","one_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorValueResolvent_denseRange","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenseRange","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Bot.bot","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.toLinearMap","DFunLike.coe","Dense","DenseRange","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists.intro","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.correspondenceOperatorValueResolvent_eq_zero_iff","GinibrePoincare.correspondenceOperatorValueResolvent_symmetric","GinibrePoincare.ginibreMeasure","Iff.mp","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsClosed.completeSpace_coe","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","LinearMap.range","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomSurjective.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.range","Set.univ","SetLike.coe","SetLike.instMembership","Submodule","Submodule.HasOrthogonalProjection.ofCompleteSpace","Submodule.instBot","Submodule.instOrderBot","Submodule.instPartialOrder","Submodule.instTop","Submodule.isClosed_topologicalClosure","Submodule.le_topologicalClosure","Submodule.mem_orthogonal'","Submodule.orthogonal","Submodule.orthogonal_eq_bot_iff","Submodule.setLike","Submodule.topologicalClosure","Submodule.topologicalClosure_coe","Subtype","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","bot_le","closure","congrArg","dense_iff_closure_eq","ext_inner_right","fact_one_le_two_ennreal","id","inner_zero_left","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instUniformSpaceSubtype","le_antisymm","propext","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorValueResolvent_eq_zero_iff","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","Iff","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","Comm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","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","Not.intro","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdInnerProductSpace","WithLp.instProdNormedAddCommGroup","WithLp.instProdSeminormedAddCommGroup","WithLp.instProdTopologicalSpace","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congrArg","congrFun'","contravariant_lt_of_covariant_le","eq_self","fact_one_le_two_ennreal","id","inferInstance","inner_zero_left","inner_zero_right","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","map_zero","mul_pos_of_neg_of_neg","neg_eq_zero","norm_eq_zero","norm_nonneg","of_eq_true","rfl","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorFixedSpace","name":"GinibrePoincare.correspondenceOperatorValueResolvent_fixed_iff_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","Iff","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Se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Group","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormResolvent_norm_le","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le.trans","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instPreorder","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp","WithLp.fst","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdNorm","WithLp.norm_fst_le","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorValueResolvent_positive","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","HPow.hPow","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instMonoid","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdNormedAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instHPow","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.symm","Eq.trans","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormResolvent_riesz","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormValue","GinibrePoincare.ginibreMeasure","HPow.hPow","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toCon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groupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.symm","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormResolvent_riesz","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormValue","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Trans.trans","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdInnerProductSpace","WithLp.instProdSeminormedAddCommGroup","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","id","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","instTransEq","real_inner_comm"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorWeakSpace","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoid.mk","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.mk","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.correspondenceOperatorWeakSpace._proof_1","GinibrePoincare.correspondenceOperatorWeakSpace._proof_10","GinibrePoincare.correspondenceOperatorWeakSpace._proof_12","GinibrePoincare.correspondenceOperatorWeakSpace._proof_2","GinibrePoincare.correspondenceOperatorWeakSpace._proof_3","GinibrePoincare.correspondenceOperatorWeakSpace._proof_4","GinibrePoincare.correspondenceOperatorWeakSpace._proof_5","GinibrePoincare.correspondenceOperatorWeakSpace._proof_6","GinibrePoincare.correspondenceOperatorWeakSpace._proof_7","GinibrePoincare.correspondenceOperatorWeakSpace._proof_9","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Set.ofPred","SetLike.instMembership","Submodule.mk","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorWeakSpace._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreMeasure","HAdd.hAdd","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","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up","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorWeakSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperatorWeakSpace_isClosed","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorWeakSpace","GinibrePoincare.ginibreMeasure","IsClosed","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"],"value_dependencies":["GinibrePoincare.isClosed_ginibre_distributional_gradient_pairs","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorOUSmoothing","name":"GinibrePoincare.correspondenceOperator_OUVariance_pos","type_dependencies":["GinibrePoincare.ginibreOUVariance","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUDecay_nonneg","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance_coe","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.pow_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","Mul","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","Non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","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperator_OUVariance_pos","GinibrePoincare.correspondenceOperator_normalized_OU_configuration_hasLaw","GinibrePoincare.drivenOUCorrection","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly._proof_4","GinibrePoincare.ginibreHamiltonianOUReferenceProcess","GinibrePoincare.ginibreHamiltonianOUReferenceProcess_scalar_assembly","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.nnreal_coe_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_eq_eval_of_eq_of_eq","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_div_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aemeasurable","Measurable.const_add","Measurable.fun_const_smul","MeasurableSMul.toMeasurableConstSMul","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_lt._simp_1","Nat.cast_pos'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","NeZero.charZero_one","NeZero.one","Neg.n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onoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.left","Bool","Bool.false","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","EuclideanSpace","Exists","Exists.casesOn","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.correspondenceOperatorFormGradient","GinibrePoincare.correspondenceOperatorFormResolvent","GinibrePoincare.correspondenceOperatorFormSpace","GinibrePoincare.correspondenceOperatorFormValue","GinibrePoincare.correspondenceOperatorGenerator_resolvent_unique","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreDistributionalWeakPair_compact_equation_complete","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreInteriorSmoothPair","GinibrePoincare.ginibreInteriorSmoothPair._proof_1","GinibrePoincare.ginibreInteriorSmoothPair._proof_2","GinibrePoincare.ginibreInteriorSmoothPair._proof_3","GinibrePoincare.ginibreInteriorSmoothPair._proof_4","GinibrePoincare.ginibreLocalWeak_adjoint_to_gradient_equation","GinibrePoincare.ginibreLocalWeak_compact_L2_coordinates_locallyIntegrable","GinibrePoincare.ginibreLocalWeak_global_distributional_pair","GinibrePoincare.ginibreLocalWeak_resolvent_global_gradient_memLp","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibreTransitionAnalytic_compact_adjoint_exists_local_gradient","GinibrePoincare.ginibre_memLp_locallyIntegrable_collisionFree","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","Iff.mpr","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_one","Nat.cast_pos'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NeZero.charZero_one","Neg","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instModule","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.isBoundedSMul","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","Trans.trans","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","WithLp.measurableSpace","WithLp.ofLp","WithTop.some","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congrArg","congrFun'","contravariant_lt_of_covariant_le","div_pos","fact_one_le_two_ennreal","fderiv","id","inferInstance","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instTopENat","instTopologicalSpaceSubtype","instTransEq","measureSpaceOfInnerProductSpace","mul_comm","one_mul","rfl","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorCfcEigenvector","name":"GinibrePoincare.correspondenceOperator_cfc_eigenvector","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","ContinuousOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Field.toDivisionRing","Field.toSemifield","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsSelfAdjoint.instContinuousFunctionalCalculus","IsStarNormal","IsStarNormal.instIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus","Membership.mem","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instCommSemiring","Real.instMonoid","Real.instZero","Real.metricSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","cfc","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHSMul","instIsTopologicalRingReal","instSMulOfMul","instStarRingReal","smulCommClass_self","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","AlgHom.toRingHom","AlgHomClas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_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Metric.mem_closure_iff","Metric.tendsto_nhds","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","Mul","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.coe_nonneg","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomIsometric.ids","RingHomSurjective.ids","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","Set.ofPred","Set.range","SetLike.coe","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","Submodule.topologicalClosure","Submodule.topologicalClosure_coe","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_pos_of_pos_of_nonneg","closure","congrArg","dist_eq_norm","dist_triangle","dist_zero_right","div_eq_mul_inv","div_le_iff\u2080","div_lt_iff\u2080","div_pos","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","lt_of_not_ge","map_sub","mul_comm","mul_le_mul_of_nonneg_right","mul_nonneg","nhds","norm_nonneg","one_div","rfl","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorErgodicScalar","name":"GinibrePoincare.correspondenceOperator_ergodic_multiplier_bound","type_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.resolventEvolutionMultiplier","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","Membership.mem","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.norm","Set","Set.Icc","Set.instMembership","Zero.toOfNat0","instHAdd","instHDiv","instHMul","instHSub"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And.left","And.right","Bool","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_nonpositive","GinibrePoincare.resolventEvolutionMultiplier_positive_formula","GinibrePoincare.resolventEvolutionMultiplier_zero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsRightCancelAdd.addRightStrictMono_of_addRightMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.le_of_le_of_eq","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_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ormedField","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.metricSpace","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.property","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_pos_of_pos_of_nonneg","cfc","cfc_const_one","cfc_id'","cfc_mul","cfc_sub","congrArg","continuousOn_const","continuousOn_id","div_pos","id","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatNat","instSMulOfMul","instStarRingReal","le_of_lt","norm_cfc_le","smulCommClass_self","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberFiniteForm","name":"GinibrePoincare.correspondenceOperator_finite_hermite_inner","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Finsupp","Finsupp.sum","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","HMul.hMul","Inner.inner","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.refl","Eq.trans","Field.toSemifield","Fin","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finsupp","Finsupp.instFunLike","Finsupp.sum","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_1","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_2","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_3","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_5","GinibrePoincare.ComplexHermite.finiteHermiteCombination._proof_6","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.Com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asurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreOUVariance","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Preorder.toLT","ProbabilityTheory.HasLaw","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instProperSpace","Complex.measurableSpace","Continuous.measurable","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousMul.measurableMul","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.correspondenceOperator_normalized_OU_hasLaw","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreGaussian_coordinate_assembly_law","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUConvolutionFunctional_ae_eq","GinibrePoincare.ginibreOUConvolutionFunctional_measurable","GinibrePoincare.ginibreOUVariance","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Measurable.aemeasurable","Measurable.const_mul","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.borelSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.comp","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun.comp","ProbabilityTheory.iIndepFun.congr","ProbabilityTheory.iIndepFun.hasLaw_pi","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorOUSmoothing","name":"GinibrePoincare.correspondenceOperator_normalized_OU_hasLaw","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUVariance","HDiv.hDiv","HMul.hMul","Inv.inv","LT.lt","MeasurableSpace","MeasureTheory.Measure","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","ProbabilityTheory.HasLaw","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","Real","Real.instInv","Real.instMul","Real.instNatCast","Real.instZero","Real.measurableSpace","Real.sqrt","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","DFunLike.coe","Decidable.decide","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.correspondenceOperator_OUVariance_pos","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_zero_hasLaw","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.nnreal_coe_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","MeasurableSpace","MeasureTheory.Measure","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.eq","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_const_mul","Prod","Prod.mk","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","True","Zero.toOfNat0","autoParam","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","eq_self","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHDiv","instHMul","instHPow","instIsCancelMulZero","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","inv_pow","le_of_lt","mul_one","mul_pos","ne_of_gt","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorOrbits","name":"GinibrePoincare.correspondenceOperator_operators_eq_on_resolvent_range","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","DFunLike.coe","DenseRange.equalizer","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.correspondenceOperatorValueResolvent_denseRange","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MetricSpace.toEMetricSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","congrFun","fact_one_le_two_ennreal","funext","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorOUSmoothing","name":"GinibrePoincare.correspondenceOperator_original_endpoint_absolutelyContinuous_volume","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Real","Real.measurableSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["And.intro","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","ENNReal","ENNReal.instTop","Eq","Eq.mp","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.correspondenceOperator_OU_endpoint_absolutelyContinuous_volume","GinibrePoincare.correspondenceOperator_endpoint_absolutelyContinuous_OU","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianMaximalLifetime","GinibrePoincare.ginibreBrownianMaximalLifetime_top_ae","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreCanonicalJointHorizonPath","GinibrePoincare.ginibreCanonicalJointHorizonPath_apply_of_global","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreHamiltonianOUReferenceHorizon","GinibrePoincare.ginibreHamiltonianOUReferenceProcess","GinibrePoincare.ginibreHamiltonianOUValue","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.AbsolutelyContinuous.trans","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_congr","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_coe","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","Subtype","Subtype.mk","Subtype.property","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","funext","id","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopologicalSpaceSubtype","le_rfl","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","name":"GinibrePoincare.correspondenceOperator_orthogonal_weak_eq_zero","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.correspondenceOperatorWeakSpace","GinibrePoincare.ginibreMeasure","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAs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ormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PolishSpace.toSecondCountableTopology","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithTop.some","Zero.toOfNat0","ae_eq_zero_of_integral_contDiff_smul_eq_zero","congrArg","fact_one_le_two_ennreal","id","instCountableFin","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSMulOfMul","instT6SpaceOfMetrizableSpace","instTopENat","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorKilledAbsoluteContinuity","name":"GinibrePoincare.correspondenceOperator_path_absolutelyContinuous_OU","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.correspondenceOperatorPathMeasurableSpace","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreCanonicalJointHorizonPath","GinibrePoincare.ginibreHamiltonianOUReferenceHorizon","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype","Subtype.mk","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["And.intro","CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","ContinuousMap","DFunLike.coe","ENNReal","ENNReal.instZero","ENNReal.ofReal","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Filter.Eventually","Filter.Eventually.of_forall","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.correspondenceOperatorPathMeasurableSpace","GinibrePoincare.ginibreActionLocalityPathMeasurable","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianFullContinuousNoise_measurable","GinibrePoincare.ginibreBrownian_original_joint_killed_compact_path_law_all_initial","GinibrePoincare.ginibreCanonicalJointHorizonPath","GinibrePoincare.ginibreCanonicalJointH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rePoincare.ginibreOriginalStochasticL2Resolvent","HDiv.hDiv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instNatCast","Real.instZero","Real.isBoundedSMul","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHDiv","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Compl.compl","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.rec","Eq.refl","Exists","Exists.casesOn","Field.toSemifield","Filter.Eventually","Filter.Eventually.mono","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreCollisionFreeCompactTest","GinibrePoincare.collisionFree_iff_not_mem_collisionSet","GinibrePoincare.collisionSet","GinibrePoincare.correspondenceOperatorValueResolvent","GinibrePoincare.correspondenceOperator_bounded_adjoint_identification","GinibrePoincare.ginibreBoundedLp_measurable_version","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","GinibrePoincare.ginibreOriginalStochasticL2Resolvent_bounded_representative","GinibrePoincare.ginibreOriginalStochasticL2Resolvent_compact_adjoint_integral","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibreStationaryContinuousTransitionMean","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Max.max","Measurable","Measurable.aestronglyMeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.of_bound","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.ae_of_a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italSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addGroup","Pi.borelSpace","Pi.continuousAdd'","Pi.instOne","Pi.instSub","Pi.instZero","Pi.isTopologicalAddGroup","Pi.measurableAdd","Pi.measurableNeg","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.seminormedAddGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PolishSpace.toSecondCountableTopology","PolynormableSpace.continuousSMul","PosMulReflectLE.toPosMulReflectLT","PosMulReflectLT","PosMulStrictMono.toPosMulMono","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","ProperSpace.isCompact_closedBall","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.instZeroLEOneClass","Real.isBoundedSMul","Real.linearOrder","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","Set.preimage","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithLp.ofLp","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientLocal.0.GinibrePoincare.correspondenceOperator_zero_gradient_local_constant._simp_1_2","_private.GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientLocal.0.GinibrePoincare.correspondenceOperator_zero_gradient_local_constant._simp_1_3","_private.GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientLocal.0.GinibrePoincare.correspondenceOperator_zero_gradient_local_constant._simp_1_4","addRightReflectLE_of_addLeftReflectLE","congr","congrArg","congrFun'","congr_arg\u2082","contravariant_lt_of_covariant_le","convex_ball","dist_comm","dist_triang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ibrePoincare.Analysis.CorrespondencePolynomialGaussian","name":"GinibrePoincare.correspondencePolynomial_contDiff","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedPolynomialEval","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidHomClass.toAddHomClass","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.conjCLE","Complex.instAdd","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","ContDiff","ContDiff.add","ContDiff.comp","ContDiff.mul","ContinuousLinearEquiv","ContinuousLinearEquiv.contDiff","ContinuousLinearEquiv.equivLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","ENat","Eq","Eq.mpr","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedPolynomialEval","GinibrePoincare.ginibreMixedPolynomialEval._proof_1","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","MvPolynomial.induction_on","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.instAdd","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","congrArg","congrFun'","contDiff_apply","contDiff_const","dite","eq_self","funext","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatNat","instTopENat","ite","ite_eq_left","ite_eq_right","map_add","map_mul","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondencePolynomialGeneratorL2","name":"GinibrePoincare.correspondencePolynomial_coulomb_memLp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.coulombPairDirection","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMixedPolynomialEval","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module",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inormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","T5Space.toT1Space","T6Space.toT5Space","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","div_eq_mul_inv","id","instCountableFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTFin","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTransEq_1","measurable_pi_apply","mul_le_mul","mul_nonneg","norm_div","norm_inv","norm_mul","norm_nonneg","norm_sub_rev","rfl","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondencePolynomialLipschitz","name":"GinibrePoincare.correspondencePolynomial_lipschitz_norm_eq","type_dependencies":["AddCommGroup.toAddCommMonoid","And","BddAbove","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Field.toSemifield","GinibrePoincare.correspondenceDifferenceQuotients","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instLE","Real.instSupSet","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set.range","SupSet.sSup","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","BddAbove","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instCharZero","Complex.instDecidableEq","Complex.instInhabited","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSub","Complex.instZero","ConditionallyCompleteLattice.toLattice","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","GinibrePoincare.correspondenceDifferenceQuotients","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LipschitzWith","LipschitzWith.norm_sub_le","LipschitzWith.of_dist_le_mul","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","MetricSpace.toEMetricSpace","MetricSpace.toPseudoMetricSpace","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNNorm.nnnorm","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat.cast_one","Nat.cast_zero","Ne","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRi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oincare.rawGinibreMeasure","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeDensity_ne_zero_ae","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermondeWeight_eq_zero_iff","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mpr","Inv.inv","InvOneClass.toInv","IsScalarTower.right","LT.lt","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.AbsolutelyContinuous.ae_le","MeasureTheory.Measure.AbsolutelyContinuous.trans","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.smul_absolutelyContinuous","MeasureTheory.Measure.withDensity","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.ae_eq","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.const_mul","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.withDensity_absolutelyContinuous","Membership.mem","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun'","eq_of_heq","eq_self","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_assoc","of_eq_true","one_mul","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondencePolynomialCoulomb","name":"GinibrePoincare.correspondencePolynomial_pair_factor","type_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.ring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instRing","Eq","Exists","Fin","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.polynomialVandermonde","HMul.hMul","HSub.hSub","LT.lt","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ring.toAddGroupWithOne","SubNegMonoid.toSub","instHMul","instHSub","instLTFin"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.commRing","AddMonoidAlgebra.instMul","AddMonoidAlgebra.ring","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.com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at","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.instSub","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","fderiv","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondencePolynomialDomain","name":"GinibrePoincare.correspondencePolynomial_projected_H1_generator","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.correspondenceOperatorGenerator","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMixedPolynomialEval","GinibrePoincare.ginibrePregenerator","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpac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ormedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondencePolynomialDifferential","name":"GinibrePoincare.correspondencePolynomial_projected_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.correspondencePolynomialDerivative","GinibrePoincare.ginibreMixedPolynomialEval","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.correspondencePolynomialDerivative","GinibrePoincare.correspondencePolynomial_contDiff","GinibrePoincare.correspondencePolynomial_derivative_eval","GinibrePoincare.ginibreMixedPolynomialEval","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpa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OrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const_mul_iff","MeasureTheory.integrable_finsetSum","MeasureTheory.integrable_norm_iff","MeasureTheory.integrable_withDensity_iff","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","MeasureTheory.volume_pi","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","MvPolynomial","MvPolynomial.as_sum","MvPolynomial.continuous_eval","MvPolynomial.eval","MvPolynomial.eval_monomial","MvPolynomial.monomial","MvPolynomial.support","NNReal","NNReal.coe_pos","NNReal.instCanonicallyOrderedAdd","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.measurableSpace","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_normOneClass","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsGaussian.memLp_id","ProbabilityTheory.gaussianPDF","ProbabilityTheory.gaussianPDFReal","ProbabilityTheory.gaussianPDFReal._proof_1","ProbabilityTheory.gaussianPDFReal_nonneg","ProbabilityTheory.gaussianPDF_lt_top","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_of_var_ne_zero","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","ProbabilityTheory.isGaussian_gaussianReal","ProbabilityTheory.measurable_gaussianPDF","ProbabilityTheory.measurable_uncurry_gaussianPDF","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.exp","Real.exp_sum","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pi","Real.pi_pos","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Real.sqrt_ne_zero'","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T6Space.toT0Space","Top.top","TopologicalSpace","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","Zero","Zero.toOfNat0","autoParam","congrArg","congrFun'","eq_of_heq","eq_self","funext","heq_of_eq","id","inferInstance","instDistr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idable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toContinuousENorm","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","FiniteDimensional","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.univ","Fintype","GinibrePoincare.correspondenceWeightedEllipticGenerator","GinibrePoincare.correspondenceWeightedEllipticMeasure","GinibrePoincare.correspondenceWeightedElliptic_integral_density","GinibrePoincare.correspondenceWeightedElliptic_locallyIntegrable","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Mathlib.Tactic.RingNF.mul_assoc_rev","Mathlib.Tactic.RingNF.nat_rawCast_1","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.IsFiniteMeasure","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.ae_of_all","MeasureTheory.integrable_finsetSum","MeasureTheory.integral","MeasureTheory.integral_add","MeasureTheory.integral_congr_ae","MeasureTheory.integral_finsetSum","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass",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rePoincare.correspondenceWeightedEllipticMeasure","HMul.hMul","HSMul.hSMul","Iff","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","Measurable.ennreal_ofReal","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integrable_withDensity_iff_integrable_smul'","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","SubNegMonoid.toAddMonoid","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun'","funext","id","iff_self","instHMul","instHSMul","le_of_lt","measureSpaceOfInnerProductSpace","of_eq_true","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticDensity","name":"GinibrePoincare.correspondenceWeightedElliptic_integral_density","type_dependencies":["BorelSpace","Continuous","Eq","FiniteDimensional","GinibrePoincare.correspondenceWeightedEllipticMeasure","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instLT","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Continuous","Continuous.measurable","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","ENNReal.ofReal_lt_top","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mpr","Eq.trans","Field.toSemifield","FiniteDimensional","GinibrePoincare.correspondenceWeightedEllipticMeasure","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","LT.lt","Measurable.ennreal_ofReal","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integral","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instDivisionRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","funext","id","instHMul","instHSMul","integral_withDensity_eq_integral_toReal_smul","le_of_lt","measureSpaceOfInnerProductSpace","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticReal","name":"GinibrePoincare.correspondenceWei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normedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","Trans.trans","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","continuous_fst","eq_self","funext","instDistribOfSemiring","instHMul","instHSub","instIsAddHaarMeasureVolume","instSecondCountableTopologyReal","instTopologicalSpaceProd","instTransEq","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_assoc","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","ContDiffBump","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","ContDiffBump","ContDiffBump.normed","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional","GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_1","GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_2","GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_3","GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_4","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_1","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_2","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHSMul","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","ContinuousAdd","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup.toContinuousAdd","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","BorelSpace","FiniteDimensional","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_1","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","BorelSpace","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Real","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toIsBoundedSMul","Real","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage._proof_4","type_dependencies":["FiniteDimensional","HasContDiffBump","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"],"value_dependencies":["ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticConvolution","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage_convolution_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSu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qFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","Metric.ball","Metric.continuousAt_iff","Metric.mem_ball","Metric.tendsto_atTop","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instLattice","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instIsStrictOrderedRing","Real.instLT","Real.instPreorder","Real.instRCLike","Real.instZero","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeSup.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","dist_eq_norm","fact_one_le_two_ennreal","half_lt_self","half_pos","id","instArchimedeanNat","instHDiv","instHSub","instInhabitedNat","instIsAddHaarMeasureVolume","instIsDirectedOrder","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","tendsto_order"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage_test_pairing","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","ContDiffBump","ContDiffBump.normed","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","GinibrePoincare.correspondenceWeighted_lebesgueL2BumpAverage","HMul.hMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike",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respondenceWeighted_lebesgueL2Translate","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","DFunLike.coe","DomAddAct","DomAddAct.instVAddSubtypeAEEqFunMemAddAddSubgroupLp","DomAddAct.mk","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","FiniteDimensional","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_1","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_2","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_3","GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_4","HVAdd.hVAdd","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Neg.neg","NegZeroClass.toNeg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","instHVAdd","instOfNatAtLeastTwo","instVAddOfAdd","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceWeightedEllipticMollification","name":"GinibrePoincare.correspondenceWeighted_lebesgueL2Translate._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","BorelSpace","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.VAddInvariantMeasure","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instVAddOfAdd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","BorelSpace","ContinuousAdd.measurableAdd","FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace","Measu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rFun'","funext","id","instArchimedeanNat","instInhabitedNat","instIsDirectedOrder","instNonemptyOfInhabited","instSecondCountableTopologyReal","nhds","secondCountableTopologyEither_of_right","tendsto_const_nhds","tendsto_nhds_unique"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsStoppingOptional","name":"GinibrePoincare.correspondence_continuous_martingale_bounded_stopping_setIntegral","type_dependencies":["And","Continuous","Eq","Filter.Eventually","InnerProductSpace.toNormedSpace","LE.le","MeasurableSet","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Integrable","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.IsStoppingTime.measurableSpace","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.ae","MeasureTheory.integral","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","UniformSpace.toTopologicalSpace","WithTop.some"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","And.left","Bool","CommMagma.toMul","CommSemiring.toNonUnitalCommSemiring","Continuous","Continuous.continuousAt","ContinuousAt.tendsto","ContinuousENorm.toENorm","Countable.LindelofSpace","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instTopologicalSpace","ENNReal.instZero","ENNReal.ofNNReal","ENNReal.one_ne_top","ENorm.enorm","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.min","Filter.atTop","Filter.atTop_neBot","Filter.mp_mem","Filter.univ_mem'","FloorSemiring.instCharZero","FloorSemiring.instZeroLEOneClass","GinibrePoincare.stoppingUpperGrid","GinibrePoincare.stoppingUpperGrid_countable_range","GinibrePoincare.stoppingUpperGrid_isStoppingTime","GinibrePoincare.stoppingUpperGrid_tendsto","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toMin","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSet","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.sub","MeasureTheory.Filtration","MeasureTheory.HasFiniteIntegral","MeasureTheory.Integrable","MeasureTheory.Integrable.uniformIntegrable_condExp","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsFiniteMeasure.sigmaFiniteFiltration","MeasureTheory.IsStoppingTime","MeasureTheory.IsStoppingTime.measurableSpace","MeasureTheory.IsStoppingTime.measurableSpace_le","MeasureTheory.IsStoppingTime.measurableSpace_le_of_le","MeasureTheory.IsStoppingTime.measurableSpace_mono","MeasureTheory.IsStoppingTime.min_const","MeasureTheory.IsStoppingTime.sigmaFinite_stopping_time","MeasureTheory.Martingale","MeasureTheory.Martingale.integrable","MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_const_of_countable_range","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MemLp","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.TendstoInMeasure","MeasureTheory.UniformIntegrable","MeasureTheory.UniformIntegrable.aestronglyMeasurable","MeasureTheory.UniformIntegrable.integrable_of_ae_tendsto","MeasureTheory.UniformIntegrable.memLp","MeasureTheory.UniformIntegrable.unifIntegrable","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.eLpNorm","MeasureTheory.eLpNorm_one_eq_lintegral_enorm","MeasureTheory.integral","MeasureTheory.lintegral","MeasureTheory.memLp_one_iff_integrable","MeasureTheory.setIntegral_condExp","MeasureTheory.setIntegral_congr_ae","MeasureTheory.stoppedValue","MeasureTheory.tendstoInMeasure_of_tendsto_ae","M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oincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_ginibre_gaussian","GinibrePoincare.correspondence_standardGaussian_cross_moment","GinibrePoincare.ginibreMeasure","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.standardComplexGaussianMeasure","HMul.hMul","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.integral","MeasureTheory.integral_map","MetricSpace.toEMetricSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instMul","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHMul","instIsTopologicalRingReal","instLTNat","instOfNatNat","instSecondCountableTopologyReal","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCurvatureComplexHessian","name":"GinibrePoincare.correspondence_gaussian_complex_hessian","type_dependencies":["Complex","Complex.instMul","Complex.instNatCast","Complex.instZero","Complex.ofReal","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.configurationNormSq","GinibrePoincare.dbarComponent","HMul.hMul","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Zero.toOfNat0","instDecidableEqFin","instHMul","ite"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.I_sq","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instT2Space","Complex.instZero","Complex.ofReal","Complex.ofReal_mul","ContDiff.mul","ContinuousLinearMap","ContinuousLinearMap.fderiv","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.smul_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.bkDirectional","GinibrePoincare.bkPartial","GinibrePoincare.bkPartial._proof_1","GinibrePoincare.bkRadial_dbar","GinibrePoincare.configurationNormSq","GinibrePoincare.coordinateDirection","GinibrePoincare.dbarComponent","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.t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GinibrePoincare.Analysis.CorrespondenceCurvatureComplexHessian","name":"GinibrePoincare.correspondence_gaussian_strict_plurisubharmonic","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instStarRing","Complex.instZero","Complex.ofReal","Complex.re","DFunLike.coe","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.configurationNormSq","GinibrePoincare.dbarComponent","HMul.hMul","LT.lt","Nat","Nat.cast","Ne","OfNat.ofNat","Pi.instZero","Real","Real.instLT","Real.instNatCast","Real.instZero","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHMul","instLTNat","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.addLeftReflectLE_of_addLeftMono","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDecidableEq","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNontrivial","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.mul_re","Complex.normSq","Complex.normSq_eq_conj_mul_self","Complex.normSq_nonneg","Complex.normSq_pos","Complex.ofReal","Complex.re","Complex.re_sum","DFunLike.coe","Decidable.byContradiction","Decidable.not_not._simp_1","Distrib.toAdd","Distrib.toMul","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mem_univ","Finset.mem_univ._simp_1","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.sum_eq_single","Finset.sum_pos'","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.configurationNormSq","GinibrePoincare.correspondence_gaussian_complex_hessian","GinibrePoincare.dbarComponent","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","IsEmpty.forall_iff._simp_1","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_eq_zero._simp_1","Nat.cast_pos","Nat.decidableExistsFin","Nat.instCommSemiring","Nat.rawCast","Ne","Ne.symm","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Pi.instZero","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedCancelAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instSub","Real.instZero","Real.partialOrder","Real.semiring","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","congr","congrArg","congrFun'","eq_false","eq_self","funext","id","implies_congr","instDecidableEqFin","instDecidableNot","instDecidableTrue","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsEmptyFalse","instIsLeftCancelAddOfAddLeftReflectLE","instLTNat","instMulZeroClassOfSemiring","inst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ow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.rawCast","Ne","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceAlgebraGenerator.0.GinibrePoincare.correspondence_generator_wirtinger_display._simp_1_1","cast","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","fderiv","id","inferInstance","instDecidableEqNat","instDecidableNot","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsCancelMulZero","instLTNat","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","mul_one","of_decide_eq_true","one_mul","one_ne_zero","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsAlmostSureStopping","name":"GinibrePoincare.correspondence_ginibre_ae_finite_strongMarkov","type_dependencies":["Complex","Complex.measurableSpace","Distrib.toAdd","Eq","Filter.Eventually","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianStateProcess","GinibrePoincare.ginibreCanonicalStateValue","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","HAdd.hAdd","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.IsStoppingTime.measurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.ae","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","Nat","Ne","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","Real","Real.measurableSpace","Subtype","Subtype.instMeasurableSpace","Top.top","WithTop","WithTop.top","WithTop.untopD","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instLTNat","instOfNatNat"],"value_dependencies":["Complex","Complex.measurableSpace","Distrib.toAdd","Eq","Exists","Exists.casesOn","Filter.Eventually","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.correspondenceBrownian_ae_finite_stopping","GinibrePoincare.correspondence_ginibre_stopping_future_past_joint_law","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianStateProcess","GinibrePoincare.ginibreCanonicalStateValue","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","HAdd.hAdd","LE.le","LT.lt","Measurable","Measurable.mono","MeasurableSpace","MeasurableSpace.instLE","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.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ing","instHAdd","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsGlobalCIR","name":"GinibrePoincare.correspondence_ginibre_global_independent_CIR_equations","type_dependencies":["And","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Exists","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasureSpace.volume","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.sqrt","Real.toNNReal","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLENat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","And","And.casesOn","And.intro","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.correspondenceCIRIntegral","GinibrePoincare.correspondenceCIRIntegral._proof_1","GinibrePoincare.correspondence_ginibre_global_independent_CIR_integrals","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasureSpace.volume","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instCommSemiring","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.sqrt","Real.toNNReal","Ring","Ring.toAddCommGroup","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopological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ormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_normOneClass","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.norm_single","PiLp.single","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.cont","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.mk","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.decidableEq","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.sqrt","Real.toNNReal","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithLp.ofLp","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceDynamicsGlobalCIR.0.GinibrePoincare.correspondence_ginibre_global_independent_CIR_integrals._proof_1_1","congrArg","congrFun'","dite","eq_self","fact_one_le_two_ennreal","instAddNat","instDecidableEqFin","instDecidableEqProd","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","lt_of_le_of_ne","nhds","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsHunt","name":"GinibrePoincare.correspondence_ginibre_random_time_continuity","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","NNReal","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.instPreorder","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","nhds"],"value_dependencies":["And","And.left","And.right","CommCStarAlgebra.toNormedCommRing","Complex","Continuous","Continuous.comp","Continuous.continuousAt","ContinuousAt.tendsto","Eq","Eq.mp","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.comp","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownianMaximalProcess_global_original_solution","GinibrePoincare.ginibreConfigurationBrownianNoise","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.StronglyAdapted","MeasureTheory.ae","Membership.mem","NNReal","NNReal.continuous_coe","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.instPreorder","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_coe","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","id","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsRestart","name":"Gini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seudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.ext","Subtype.instMeasurableSpace","Subtype.property","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instLTNat","instOfNatNat","le_rfl","measurable_fst","measurable_snd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsGlobalCIR","name":"GinibrePoincare.correspondence_global_CIR_integral_of_local","type_dependencies":["And","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Exists","Filter.Eventually","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.correspondenceCIRIntegral","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreHamiltonian","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.sqrt","Real.toNNReal","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","And","And.casesOn","And.right","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Compl.compl","Complex","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionRing.toRing","EDist.edist","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instLE","ENNReal.instLinearOrder","ENNReal.instPartialOrder","ENNReal.instT5Space","ENNReal.instTopologicalSpace","ENNReal.instZero","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Filter.atTop_neBot","Filter.mp_mem","Filter.univ_mem'","Fin","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.sum","Finset.sum_congr","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.correspondenceCIRIntegral","GinibrePoincare.correspondenceCIRIntegral._proof_1","GinibrePoincare.correspondence_measure_compl_of_ae_exhaustion","GinibrePoincare.correspondence_tendstoInMeasure_of_exhaustion","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop_exhausts_ae","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop_survival_measurable","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_le","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibre_tendstoInMeasure_indicator","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_le_end","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMo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orrespondenceDynamicsGlobalCIR.0.GinibrePoincare.correspondence_global_CIR_integral_of_local._proof_1_1","_private.GinibrePoincare.Analysis.CorrespondenceDynamicsGlobalCIR.0.GinibrePoincare.correspondence_global_CIR_integral_of_local._simp_1_2","congr","congrArg","congrFun","congrFun'","dite","eq_false","eq_self","funext","id","iff_false","inferInstance","instAddNat","instArchimedeanNat","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInhabitedNat","instIsDirectedOrder","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","intervalIntegral.integral_congr","le_add_of_nonneg_right","le_rfl","min_eq_left","neg_eq_zero","nhds","not_le","of_eq_true","rfl","sub_eq_zero_of_eq","tendsto_const_nhds_iff._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCurvatureHessian","name":"GinibrePoincare.correspondence_hamiltonian_interaction_hessian","type_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instStarRing","Complex.re","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreInteractionPotential","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.normedField","Real.pseudoMetricSpace","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.re","ContDiff","ContDiff.contDiffAt","ContDiff.differentiable","ContDiffAt","ContDiffAt.differentiableAt","ContDiffAt.fderiv_right","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.add_apply","ContinuousLinearMap.continuousConstSMul","ContinuousLinearMap.distribMulAction","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.module","ContinuousLinearMap.smulCommClass","ContinuousLinearMap.sm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pleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceCurvatureNegativeTest.0.GinibrePoincare.correspondence_pointwise_deficit_negative_compact_test._proof_1_1","_private.GinibrePoincare.Analysis.CorrespondenceCurvatureNegativeTest.0.GinibrePoincare.correspondence_pointwise_deficit_negative_compact_test._simp_1_2","addRightReflectLE_of_addLeftReflectLE","congrArg","congrFun'","contravariant_lt_of_covariant_le","div_pos","eq_self","even_two_mul","fderiv","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLENat","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopENat","le_of_lt","lt_of_lt_of_le","lt_of_not_ge","mul_nonneg","mul_nonneg_of_nonpos_of_nonpos","nhds","not_false_eq_true","of_eq_true","one_mul","pow_pos","pseudoMetricSpacePi","rfl","sq_nonneg","sub_eq_zero_of_eq","tsupport","tsupport_mul_subset_left","zero_add","zero_apply","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCurvatureDeficit","name":"GinibrePoincare.correspondence_pointwise_interaction_deficit","type_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","ContDiff","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBochnerGradient","GinibrePoincare.ginibreBochnerHessianSquare","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.ginibrePointwiseGamma","GinibrePoincare.ginibrePointwiseGammaTwo","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast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ommon.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.rawCast","Ne","NeZero.one","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsDomain","Real.instIsOrderedRing","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","cast","congr","congrArg","congr_arg","congr_arg\u2082","div_one","eq_self","fderiv","id","inferInstance","instCommCStarAlgebraComplex","instDecidableEqNat","instDecidableNot","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsCancelMulZero","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","isReduced_of_noZeroDivisors","mul_left_cancel\u2080","mul_one","neg_eq_zero","neg_mul","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","pow_ne_zero","rfl","starRingEnd","sub_eq_zero_of_eq","sub_neg_eq_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAlgebraCenterCovariance","name":"GinibrePoincare.correspondence_standardGaussian_cross_moment","type_dependencies":["Complex","Complex.im","Complex.measurableSpace","Complex.re","Eq","GinibrePoincare.standardComplexGaussianMeasure","HMul.hMul","InnerProductSpace.toNormedSpace","MeasureTheory.integral","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAdd","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatC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","of_eq_true","one_div","pow_two","pow_zero","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDynamicsLocalization","name":"GinibrePoincare.correspondence_tendstoInMeasure_of_exhaustion","type_dependencies":["Compl.compl","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.Tendsto","Filter.atTop","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.real","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","OfNat.ofNat","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.metricSpace","Real.pseudoMetricSpace","Set","Set.indicator","Set.instCompl","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.intro","Bool","Bool.false","Classical.propDecidable","CommRing.toRing","CommSemiring.toSemiring","Compl.compl","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","Filter.Eventually","Filter.Eventually.exists","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.eventually","Filter.atTop","Filter.atTop_neBot","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","LT.lt.trans_le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.real","MeasureTheory.TendstoInMeasure","MeasureTheory.measureReal_mono","MeasureTheory.measureReal_nonneg","MeasureTheory.measureReal_union_le","MeasureTheory.measure_ne_top","MeasureTheory.tendstoInMeasure_iff_measureReal_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","Mul","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreord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inormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","fderiv","fderiv_mul","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instSMulOfMul","rfl","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.dbarComponent_mul_conj","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instStarRing","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHAdd","instHMul","instInnerProductSpaceRealComplex","starRingEnd"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.differentiable_conj","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.comp","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent_mul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.dbarComponent_normalizedVandermondeTransform","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instInv","Complex.instMul","Complex.instNormedField","Complex.ofReal","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.vandermonde","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSp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ormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instNatCast","Real.instRCLike","Real.normedField","Real.sqrt","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.AlternativeSlaterLowering.0.GinibrePoincare.slater_dbar_const_mul","_private.GinibrePoincare.Analysis.AlternativeSlaterLowering.0.GinibrePoincare.slater_dbar_finset_sum","congrArg","congrFun'","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instCommCStarAlgebraComplex","instDecidableEqFin","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","instLTNat","instMulNat","instOfNatNat","instOneENat","instSubNat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.dbarComponent_vandermonde","type_dependencies":["Complex","Complex.instZero","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.vandermonde","Nat","OfNat.ofNat","Zero.toOfNat0"],"value_dependencies":["Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent_eq_zero_of_differentiable_complex","GinibrePoincare.differentiable_vandermonde","GinibrePoincare.vandermonde","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","name":"GinibrePoincare.dbarComponent_zero_of_eventuallyZero","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Eq","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivInvMonoid.toInv","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.fderiv_eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congr","congrArg","congrFun","congrFun'","eq_self","fderiv","fderiv_fun_const","id","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","nhds","of_eq_true","one_div","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultInterior","name":"GinibrePoincare.dbarComponent_zero_of_notMem_tsupport","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.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p.toAddCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toMul","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarNormSq","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.normSq_dbarComponent_ofReal","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","congrArg","congrFun'","fderiv","id","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.dbarNormSq_ofReal_eq_realGradientNormSq","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.ofReal","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarNormSq","GinibrePoincare.realGradientNormSq","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHDiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.dbarNormSq","GinibrePoincare.dbarNormSq_ofReal","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.realGradientNormSq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","congrArg","fderiv","id","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.dbarOnePublic_conj_normalizedEval","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Eq","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.normalizedEval","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Real.sqrt","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat","starRingEnd"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Eq","Eq.mpr","Eq.refl","GinibrePoincare.ComplexHermite.dbarOnePublic","GinibrePoincare.ComplexHermite.dbarOne_normalizedEval_public","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.conj_normalizedEval_swap","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Real.sqrt","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","congrArg","funext","id","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumFactorization","name":"GinibrePoincare.decomposition_eq","type_dependencies":["Complex","Complex.instAdd","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.projectToCenterLine","GinibrePoincare.projectToOrthogonal","HAdd.hAdd","Nat","instHAdd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instNatCast","Complex.instSub","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.projectToCenterLine","GinibrePoincare.projectToOrthogonal","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Ring","Ring.toAdd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},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexCDF","name":"GinibrePoincare.densityCDF_strictMonoOn","type_dependencies":["Continuous","GinibrePoincare.densityCDF","LT.lt","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instPreorder","Real.instZero","Real.measureSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set.Ioi","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Continuous","Continuous.continuousOn","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Field.toSemifield","GinibrePoincare.densityCDF","GinibrePoincare.densityCDF_continuous","GinibrePoincare.densityCDF_hasDerivAt","HasDerivAt.deriv","InnerProductSpace.toNormedSpace","IsStrictOrderedModule.toPosSMulStrictMono","IsStrictOrderedRing.toIsStrictOrderedModule","LT","LT.lt","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.Ioi","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","convex_Ioi","deriv","id","instMulZeroClassOfSemiring","interior","interior_subset","strictMonoOn_of_deriv_pos"]},{"kind":"definition","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile","type_dependencies":["Eq","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"],"value_dependencies":["Eq","GinibrePoincare.increasingCDFQuantileOn","Membership.mem","OfNat.ofNat","One.toOfNat1","Real","Real.decidableLT","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.decidableMemIoo","Set.image","Set.instMembership","StrictMonoOn","Zero.toOfNat0","ite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.densityQuantileProfile","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.densityQuantileProfile","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile.eq_1","type_dependencies":["Eq","GinibrePoincare.densityQuantileProfile","GinibrePoincare.increasingCDFQuantileOn","Membership.mem","OfNat.ofNat","One.toOfNat1","Real","Real.decidableLT","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.decidableMemIoo","Set.image","Set.instMembership","StrictMonoOn","Zero.toOfNat0","ite"],"value_dependencies":["Eq","Eq.refl","GinibrePoincare.densityQuantileProfile","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Ioo","Set.image","StrictMonoOn","Zero.toOfNat0"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile_contDiffAt_two","type_dependencies":["CommSemiring.toSemiring","ContDiffAt","ContDiffOn","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Field.toSemifield","GinibrePoincare.densityQuantileProfile","HasDerivAt","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Ioo","Set.OrdConnected","Set.image","Set.instMembership","StrictMonoOn","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","ContDiffAt.congr_of_eventuallyEq","ContDiffOn","ContDiffOn.comp","ContDiffOn.contDiffAt","ContDiffOn.of_le","DenselyNormedField.toNontriviallyNormedField","DistribLattice.toLattice","ENat","ENat.instNatCast","Eq","Eq.refl","Field.toSemifield","Function.comp","GinibrePoincare.densityQuantileProfile","GinibrePoincare.densityQuantileProfile_eventually_eq","GinibrePoincare.increasingCDFQuantileOn","GinibrePoincare.increasingCDFQuantileOn_contDiffOn_two","GinibrePoincare.increasingCDFQuantileOn_mem","HasDerivAt","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOpen.mem_nhds","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instIsOrderedAddMonoid","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Ioo","Set.OrdConnected","Set.image","Set.instMembership","StrictMonoOn","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instDistribLatticeOfLinearOrder","instHasSolidNormReal","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPolynormableSpace","isOpen_Ioo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile_eventually_eq","type_dependencies":["Eq","Filter.EventuallyEq","Function.comp","GinibrePoincare.densityQuantileProfile","GinibrePoincare.increasingCDFQuantileOn","Membership.mem","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Ioo","Set.image","Set.instMembership","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","nhds"],"value_dependencies":["DistribLattice.toLattice","Eq","Eq.trans","Filter.mp_mem","Filter.univ_mem'","Function.comp","GinibrePoincare.densityQuantileProfile","GinibrePoincare.increasingCDFQuantileOn","HasSolidNorm.orderClosedTopology","IsOpen.mem_nhds","Lattice.toSemilatticeInf","Membership.mem","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.decidableLT","Real.instIsOrderedAddMonoid","Real.instOne","Real.instPreorder","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","Set","Set.Ioo","Set.decidableMemIoo","Set.image","Set.instMembership","Set.ofPred","StrictMonoOn","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","eq_true","id","instDistribLatticeOfLinearOrder","instHasSolidNormReal","isOpen_Ioo","ite_eq_left_of_eq_true","nhds","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexQuantileCalculus","name":"GinibrePoincare.densityQuantileProfile_hasDerivAt","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","GinibrePoincare.densityQuantileProfile","GinibrePoincare.increasingCDFQuantileOn","HMul.hMul","HasDerivAt","InnerProductSpace.toNormedSpace","Membership.mem","Ne","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Ioo","Set.OrdConnected","Set.image","Set.instMembership","StrictMonoOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","instHMul","instPolynormableSpace"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Function.comp","GinibrePoincare.densityQuantileProfile","GinibrePoincare.densityQuantileProfile_eventually_eq","GinibrePoincare.increasingCDFQuantileOn","GinibrePoincare.increasingCDFQuantileOn_hasDerivAt","GinibrePoincare.increasingCDFQuantileOn_mem","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HasDerivAt","HasDerivAt.comp","HasDerivAt.congr_of_eventuallyEq","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Ne","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instField","Real.instInv","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","Semifield.toCommGroupWithZero","Semifield.toCommSemir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UnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHSub","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instInv","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.differentiableAt","ContinuousLinearMap.funLike","ContinuousLinearMap.proj","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.comp","DifferentiableAt.sub","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","differentiableAt_inv","instHSub","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.differentiable_complexRadius","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.differentiable_conj","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.differentiable","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.const_mul","Differentiable.fun_comp","Differentiable.fun_mul","Differentiable.fun_sub","Differentiable.fun_sum","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.complexRadius_eq","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.cast","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","Ring.toAddCommGroup","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","congr","congrArg","differentiable_apply","eq_self","funext","id","instHMul","instHSub","instInnerProductSpaceRealComplex","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDifferentiability","name":"GinibrePoincare.differentiable_holomorphicHermite_series","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","HMul.hMul","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instLTNat","instOfNatNat","tsum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Bool","Bool.false","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.ofReal","ContDiff.differentiable_one","ContDiffAt.differentiableAt_one","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instSMul","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.topologicalSpace","Convex.isPreconnected","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.const_mul","Differentiable.fun_comp","Differentiable.fun_pow","DifferentiableAt","DifferentiableAt.const_mul","DifferentiableAt.fun_comp'","DifferentiableAt.fun_pow","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized_zero_right","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.norm_fderiv_holomorphicHermite_le","GinibrePoincare.summable_holomorphicHermite_series","GinibrePoincare.summable_tensor_holomorphicHermite_bound","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasFDerivAt","HasFDerivAt.differentiableAt","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","LE.le","LE.le.trans","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.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congrFun'","contDiffAt_apply","contDiffAt_prod","contDiff_apply","contDiff_prod","convex_ball","differentiableAt_apply","differentiableAt_pi''","differentiable_apply","differentiable_pi''","fderiv","fderiv_const_mul","funext","hasFDerivAt_tsum_of_isPreconnected","id","inferInstance","instAddNat","instContinuousSMulForall","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instIsRCLikeNormedField","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPolynormableSpace","instSMulCommClassOfIsScalarTower","le_max_left","le_max_right","le_of_not_gt","mul_assoc","mul_le_mul","neg_neg_of_pos","norm_le_pi_norm","norm_lt_of_mem_ball","norm_nonneg","norm_smul","pseudoMetricSpacePi","rfl","tsum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialChainRule","name":"GinibrePoincare.differentiable_observablePolynomial","type_dependencies":["Complex","Complex.addCommGroup","Complex.instCommSemiring","Complex.instNormedField","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Differentiable","Fintype","GinibrePoincare.observablePolynomial","InnerProductSpace.toNormedSpace","MvPolynomial","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidHomClass.toAddHomClass","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.add","Differentiable.mul","Distrib.toAdd","Eq","Eq.mpr","Eq.trans","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Fintype","GinibrePoincare.observablePolynomial","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.eval_X","MvPolynomial.induction_on","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Pi.instAdd","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toNonUnitalRingHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","differentiable_const","eq_self","funext","id","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","map_add","map_mul","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SumRadiusCoordinates","name":"GinibrePoincare.differentiable_sumRadiusCoordinate","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.sumRadiusCoordinate","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNo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.Configuration","Nat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instSub","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset.Ioi","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexSecondDirectionalDerivative","GinibrePoincare.coordinateDirection","GinibrePoincare.coulombPairDirection","GinibrePoincare.directComplexGinibrePregenerator._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGeneratorCalculus","name":"GinibrePoincare.directComplexGinibrePregenerator._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGeneratorCalculus","name":"GinibrePoincare.directComplexGinibrePregenerator.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instSub","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset.Ioi","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexSecondDirectionalDerivative","GinibrePoincare.coordinateDirection","GinibrePoincare.coulombPairDirection","GinibrePoincare.directComplexGinibrePregenerator","GinibrePoincare.directComplexGinibrePregenerator._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.directComplexGinibrePregenerator","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CompactLipschitzLSIExtension","name":"GinibrePoincare.directionalEnergy","type_dependencies":["Fintype","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Finset.sum","Finset.univ","Fintype","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddComm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italNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.id","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","GinibrePoincare.dolbeaultBoundaryLpOperator","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","List","List.below","List.cons","List.nil","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PProd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instRCLike","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","Unit","WithTop.some","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat","measureSpaceOfInnerProductSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","name":"GinibrePoincare.dolbeaultBoundaryLpComposition._sunfold","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousL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ormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","congrArg","fact_one_le_two_ennreal","id","instCountableFin","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","name":"GinibrePoincare.dolbeaultBoundaryLpOperator","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","GinibrePoincare.dolbeaultBoundaryLpOperator._proof_1","GinibrePoincare.dolbeaultCutoffLpOperator","GinibrePoincare.planarDbar","GinibrePoincare.planarDbar_compact","HasCompactSupport","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","name":"GinibrePoincare.dolbeaultBoundaryLpOperator._proof_1","type_dependencies":["Complex","Comple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e.dolbeaultBoundedMultiplierLinear._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplier","name":"GinibrePoincare.dolbeaultBoundedMultiplierValue","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Filter.Eventually","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultOrdinaryL2","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Nat","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultBoundedMultiplierValue._proof_1","GinibrePoincare.dolbeaultBoundedMultiplierValue._proof_2","GinibrePoincare.dolbeaultBoundedMultiplier_memLp","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HMul.hMul","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplier","name":"GinibrePoincare.dolbeaultBoundedMultiplierValue._proof_1","type_dependencies":["Complex","Comple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","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_neg","Membership.mem","Metric.closedBall","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNorm","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.Function.module","Pi.addCommGroup","Pi.instAdd","Pi.instMul","Pi.instZero","Pi.normedAddCommGroup","Pi.normedRing","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.seminormedAddGroup","Pi.single","Pi.topologicalSpace","Preorder.toLE","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instLE","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungInverse.0.GinibrePoincare.dolbeaultCauchyGreenL2_weak_inverse._simp_1_1","congr","congrArg","congrFun'","continuous_const","dist_zero_right","dite","eq_self","fact_one_le_two_ennreal","fderiv","id","inferInstance","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","instZeroENat","measureSpaceOfInnerProductSpace","neg_zero","not_false_eq_true","of_eq_true","pseudoMetricSpacePi","rfl","tsupport"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","name":"GinibrePoincare.dolbeaultCompactBound","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Continuous","HasCompactSupport","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Classical.choose","Complex","Complex.instNorm","Complex.instNormedField","Complex.instZero","Continuous","GinibrePoincare.dolbeault_compact_continuous_bound","HasCompactSupport","LE.le","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","name":"GinibrePoincare.dolbeaultCompactBound_spec","type_dependencies":["Complex","Complex.instNorm","Complex.instNormedField","Complex.instZero","Continuous","GinibrePoincare.dolbeaultCompactBound","HasCompactSupport","LE.le","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Classical.choose_spec","Complex","Complex.instNorm","Complex.instNormedField","Complex.instZero","Continuous","GinibrePoincare.dolbeault_compact_continuous_bound","HasCompactSupport","LE.le","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instCommSemiring","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype"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edRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing._proof_4","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","SMulCommClass","Semifield.toCommSemiring","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing._proof_5","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instRCLike","ContinuousConstSMul","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Distrib.toMul","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instDistribOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing._proof_6","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing._proof_7","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instCommSemiring","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCompactPairing._proof_6","HasCompactSupport","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace","starRingEnd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.continuous_conj","Complex.instCommSemiring","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Continuous","Continuous.comp","Continuous.memLp_of_hasCompactSupport","DFunLike.coe","ENNReal"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omplex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.rec","Eq.refl","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCompactPairing","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","name":"GinibrePoincare.dolbeaultCompactPairing.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCompactPairing","GinibrePoincare.dolbeaultCompactPairing._proof_1","GinibrePoincare.dolbeaultCompactPairing._proof_2","GinibrePoincare.dolbeaultCompactPairing._proof_3","GinibrePoincare.dolbeaultCompactPairing._proof_4","GinibrePoincare.dolbeaultCompactPairing._proof_5","GinibrePoincare.dolbeaultCompactPairing._proof_6","GinibrePoincare.dolbeaultCompactPairing._proof_7","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.toLp","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAd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aultCoordinateConvolution_compact_test","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCoordinateConvolution","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instSub","Pi.single","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instDecidableEqFin","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCompactPairing","GinibrePoincare.dolbeaultCompactPairing_eq_integral","GinibrePoincare.dolbeaultCoordinateConvolution","GinibrePoincare.dolbeaultCoordinateConvolution_pairing","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","GinibrePoincare.dolbeaultTranslateL2","GinibrePoincare.dolbeaultTranslateL2_ae","HMul","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instSub","Pi.single","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAd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ubini","name":"GinibrePoincare.dolbeaultCoordinateConvolution_test_fubini","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instAdd","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCoordinateConvolution","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HAdd.hAdd","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instAdd","Pi.single","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instDecidableEqFin","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddZero.toAdd","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","Bornology.IsBounded.exists_norm_le","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","Continuous","Continuous.add","Continuous.aestronglyMeasurable","Continuous.comp","ContinuousAdd.measurableAdd","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCoordinateConvolution","GinibrePoincare.dolbeaultCoordinateConvolution_compact_test","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.isCompact_range","InnerProductSpace.toNormedSpace","IsCompact.isBounded","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.comp_fst","MeasureTheory.AEStronglyMeasurable.comp_snd","MeasureTheory.AEStronglyMeasurable.mul","MeasureTheory.Integrable","MeasureTheory.Integrable.aestronglyMeasurable","MeasureTheory.Integrable.const_mul","MeasureTheory.Integrable.mono'","MeasureTheory.Integrable.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AddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","Pi.addGroup","Pi.instSub","Pi.isTopologicalAddGroup","Pi.measurableAdd","Pi.opensMeasurableSpace","Pi.single","Pi.single_eq_of_ne","Pi.single_eq_same","Pi.topologicalSpace","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.opensMeasurableSpace","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformSpace.toTopologicalSpace","Zero","Zero.toOfNat0","autoParam","congrArg","congrFun'","continuous_const","continuous_fst","continuous_pi","continuous_snd","dite","funext","id","instCountableFin","instDecidableEqFin","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instSeparatelyContinuousAddOfContinuousAdd","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","norm_mul","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultHomotopy","name":"GinibrePoincare.dolbeaultCoordinateSlice_dbar","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dolbeaultReplaceCoordinate","GinibrePoincare.planarDbar","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instT2Space","Complex.instZero","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.id","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.prod","ContinuousLinearMap.zero","ContinuousLinearMap.zero_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DivInvMonoid.toDiv","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.dolbeaultReplaceCoordinate","GinibrePoincare.dolbeaultReplaceCoordinate_vertical","GinibrePoincare.planarDbar","GinibrePoincare.plana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arableSpace","UniformSpace.toTopologicalSpace","WithTop.some","fact_one_le_two_ennreal","instCountableFin","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.right","BorelSpace.opensMeasurable","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.comp","ContDiff.continuous","ContDiff.mul","Continuous.aestronglyMeasurable","Continuous.comp","Continuous.memLp_of_hasCompactSupport","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultBoundedMultiplierValue","GinibrePoincare.dolbeaultBoundedMultiplier_ae","GinibrePoincare.dolbeaultCauchyGreenL2","GinibrePoincare.dolbeaultCauchyGreenL2_smooth_compact_representative","GinibrePoincare.dolbeaultCompactBound","GinibrePoincare.dolbeaultCompactBound_spec","GinibrePoincare.dolbeaultCoordinateConvolutionPointwise","GinibrePoincare.dolbeaultCutoffLpMultiplier","GinibrePoincare.dolbeaultCutoffLpOperator","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","GinibrePoincare.dolbeaultTruncatedCauchyGreen","GinibrePoincare.dolbeaultTruncatedCutoff","HMul.hMul","HasCompactSupport","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsFiniteMeasureOnCompactsForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.ae_of_all","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instLE","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","WithTop.some","congrArg","contDiff_apply","continuous_apply","fact_one_le_two_ennreal","id","instCountableFin","instHMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","name":"GinibrePoincare.dolbeaultCylinder","type_dependencies":["Complex","Fin","Finset","GinibrePoincare.Configuration","Nat","Set"],"value_dependencies":["Complex","Fin","Finset","Finset.instSetLike","GinibrePoincare.Configuration","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SetLike.instMembership"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","name":"GinibrePoincare.dolbeaultCylinder.eq_1","type_dependencies":["Complex","Eq","Fin","Finset","Finset.instSetLike","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCylinder","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SetLike.instMembership"],"value_dependencies":["Complex","Eq.refl","Fin","Finset","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCylinder","Nat","Set"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","name":"GinibrePoincare.dolbeaultCylinder_isOpen","type_dependencies":["Complex","Complex.instNormedField","Fin","Finset","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCylinder","IsOpen","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","Eq","Eq.mpr","Eq.refl","Eq.trans","Fin","Finset","Finset.instSetLike","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCylinder","Iff","IsOpen","IsOpen.preimage","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.ext","Set.iInter","Set.instMembership","Set.mem_iInter._simp_1","Set.mem_preimage._simp_1","Set.preimage","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","congrArg","continuous_apply","forall_congr","id","iff_self","implies_congr","isOpen_biInter_finset","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundary","name":"GinibrePoincare.dolbeaultCylinder_replace","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultCylinder","GinibrePoincare.dolbeaultReplaceCoordinate","InnerProductSpace.toNormedSpace","Inter.inter","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Not","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instInter","Set.instMembership","SetLike.instMembership","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instTopologicalSpaceProd"],"value_dependencies":["And.intro","And.left","And.right","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Decidable","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","False","Fin","Fin.fintype","Finset"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ormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Filter","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultPiBump_convolution_ae","GinibrePoincare.dolbeaultPiBump_convolution_memLp","GinibrePoincare.piL2BumpAverage","GinibrePoincare.piL2BumpAverage_tendsto","GinibrePoincare.piPlanarBump","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.convolution","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMollifierPairing","name":"GinibrePoincare.dolbeaultPiBump_convolution_test","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","Continuous","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.piPlanarBump","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","MeasureTheory.integral","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHSub","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRi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inibrePoincare.Configuration","GinibrePoincare.dolbeaultCutoffLpOperator._proof_1","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultPrimitiveLp","HasCompactSupport","InnerProductSpace.toNormedSpace","List","List.cons","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"GinibrePoincare.dolbeaultPrimitiveLp.eq_def","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultBoundaryLpComposition","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","GinibrePoincare.dolbeaultCutoffLpOperator","GinibrePoincare.dolbeaultCutoffLpOperator._proof_1","GinibrePoincare.dolbeaultCutoffLpOperator._proof_2","GinibrePoincare.dolbeaultCutoffLpOperator._proof_4","GinibrePoincare.dolbeaultCutoffLpOperator._proof_5","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","GinibrePoincare.dolbeaultPrimitiveLp","GinibrePoincare.dolbeaultPrimitiveLp._proof_1","HAdd.hAdd","HasCompactSupport","InnerProductSpace.toNormedSpace","List","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","Unit","WithTop.some","Zero.toOfNat0","fact_one_le_two_ennreal","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultBoundaryLpComposition","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","GinibrePoincare.dolbeaultCutoffLpOperator","GinibrePoincare.dolbeaultCutoffLpOperator._proof_1","GinibrePoincare.dolbeaultCutoffLpOperator._proof_2","GinibrePoincare.dolbeaultCutoffLpOperator._proof_4","GinibrePoincare.dolbeaultCutoffLpOperator._proof_5","GinibrePoincare.dolbeaultOrdinaryL2","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inormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplierComposition","name":"GinibrePoincare.dolbeaultResidualOperator._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dolbeaultResidualOperator._proof_2","GinibrePoincare.dolbeaultResidualOperator._proof_4","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplierComposition","name":"GinibrePoincare.dolbeaultResidualOperator._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplierComposition","name":"GinibrePoincare.dolbeaultResidualOperator._proof_7","type_dependencies":["Complex","Complex.instSemiring","RingHom.id","RingHomCompTriple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oDivisionAddCommMonoid","And.right","CompleteSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","GinibrePoincare.drivenBoundedNoiseExtension._proof_1","GinibrePoincare.drivenBoundedNoiseSpace","GinibrePoincare.drivenBoundedNoiseSpace._proof_1","LE.le","Membership.mem","Neg.neg","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.projIcc","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenBoundedNoiseExtension_sub_norm_le","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CompleteSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.instNorm","ContinuousMap.instSubOfContinuousSub","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","HSub.hSub","IsTopologicalAddGroup.to_continuousSub","LE.le","Membership.mem","Neg.neg","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instLE","Real.instNeg","Real.instOne","Real.instPreorder","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toSub","Subtype.val","UniformSpace.toTopologicalSpace","compactSpace_Icc","instHSub","instOrderTopologyReal","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CompleteSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.instSubOfContinuousSub","ContinuousMap.norm_coe_le_norm","GinibrePoincare.drivenBoundedNoiseExtension._proof_1","GinibrePoincare.drivenBoundedNoiseSpace","HSub.hSub","IsTopologicalAddGroup.to_continuousSub","Membership.mem","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instNeg","Real.instOne","Real.instPreorder","Real.linearOrder","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.projIcc","SubNegMonoid.toSub","Subtype.val","UniformSpace.toTopologicalSpace","compactSpace_Icc","instHSub","instOrderTopologyReal","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenBoundedNoiseExtension_zero","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CompleteSpace","ContinuousMap","Eq","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","Membership.mem","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","And","And.left","Bool","Bool.true","CompleteSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mpr","Eq.refl","Eq.trans","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseExtension._proof_1","GinibrePoincare.drivenBoundedNoiseSpace","GinibrePoincare.drivenBoundedNoiseSpace._proof_1","Int","Int.negOfNat","Int.ofNat","LE.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_le_true","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat.cast_one","Nat.cast_zero","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instIsOrderedRing","Real.instLE","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.mem_Icc._simp_1","Set.projIcc","Set.projIcc_of_mem","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","UniformSpace.toTopologicalSpace","Zero.toOfNat0","and_self","congr","congrArg","eq_true","id","instDistribLatticeOfLinearOrder","instTopologicalSpaceSubtype","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenBoundedNoiseSpace","type_dependencies":["ContinuousMap","Membership.mem","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instNeg","Real.instOne","Real.instPreorder","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","And","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","GinibrePoincare.drivenBoundedNoiseSpace._proof_1","LE.le","Membership.mem","Neg.neg","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenBoundedNoiseSpace._proof_1","type_dependencies":["Membership.mem","Neg.neg","OfNat.ofNat","One.toOfNat1","Real","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Icc","Set.instMembership","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","And","Bool","Bool.true","Eq.refl","Eq.trans","Int","Int.negOfNat","Int.ofNat","LE.le","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_le_true","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat.cast_one","Nat.cast_zero","Neg.neg","NegZeroClass.toNeg","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instIsOrderedRing","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.partialOrder","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Set","Set.Icc","Set.instMembership","Set.mem_Icc._simp_1","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","True.intro","Zero.toOfNat0","and_self","congr","congrArg","eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenContinuousNoise_continuous_local_flow","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.intro","CompleteSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.instMetricSpace","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","Eq","Exists","GT.gt","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","HAdd.hAdd","HMul.hMul","LE.le","LT.lt.le","LipschitzWith","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real"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inormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","Set","Set.Elem","Set.Icc","Set.instMembership","Set.projIcc","Set.projIcc_of_mem","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Subtype.mk","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","continuous_projIcc","id","instDistribLatticeOfLinearOrder","instHAdd","instHMul","instHSub","instMulZeroClassOfSemiring","instOrderTopologyReal","instTopologicalSpaceSubtype","intervalIntegral","le_antisymm","le_refl","le_rfl","norm_eq_zero","norm_le_zero_iff._simp_1","norm_nonneg","norm_zero","sub_eq_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","name":"GinibrePoincare.drivenContinuousNoise_measurable_local_flow","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.intro","CompleteSpace","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instFunLike","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","Eq","Exists","GT.gt","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","HAdd.hAdd","LE.le","LT.lt.le","LipschitzWith","Measurable","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","NNReal","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.projIcc","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","instHAdd","instTopologicalSpaceSubtype","intervalIntegral","le_rfl"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.casesOn","And.intro","CompleteSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous.borel_measurable","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instFunLike","ContinuousMap.instMetricSpace","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","Eq","Exists","Exists.casesOn","Exists.intro","GT.gt","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","GinibrePoincare.drivenContinuousNoise_continuous_local_flow","GinibrePoincare.drivenContinuousNoise_local_flow_causal","HAdd.hAdd","HMul.hMul","LE.le","LT.lt.le","LipschitzWith","LipschitzWith.continuous","Measurable","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.exp_pos","Real.instConditionallyCompleteLinearOrder","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.projIcc","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","compactSpace_Icc","instHAdd","instHMul","instOrderTopologyReal","instPseudoEMetricSpaceSubtype","instTopologicalSpaceSubtype","intervalIntegral","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathClosedHittingTime","name":"GinibrePoincare.drivenContinuous_closed_hitting_le_iff","type_dependencies":["And","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","Continuous","Exists","Iff","IsClosed","LE.le","MeasureTheory.hittingBtwn","Membership.mem","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Set","Set.Icc","Set.instMembership","TopologicalSpace","Zero.toOfNat0"],"value_dependencies":["And","And.casesOn","And.intro","And.left","And.right","Classical.propDecidable","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","Condi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symm","le_of_not_gt","not_le_of_gt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathClosedHittingTime","name":"GinibrePoincare.drivenContinuous_norm_le_until_hitting","type_dependencies":["ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","Continuous","LE.le","MeasureTheory.hittingBtwn","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SeminormedAddCommGroup.toPseudoMetricSpace","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","And.left","And.right","Bot.bot","CommRing.toRing","CommSemiring.toSemiring","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderInf.toInfSet","ConditionallyCompletePartialOrderSup.toPartialOrder","Continuous","Continuous.continuousOn","Continuous.norm","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.ge","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists.casesOn","False","False.elim","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","LE.le.trans","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.hittingBtwn","MeasureTheory.hittingBtwn_le","MeasureTheory.hittingBtwn_le_of_mem","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instDenselyOrdered","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","Not","OfNat.ofNat","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.decidableLE","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instLT","Real.instPreorder","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.image","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","bot_le","congrArg","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemi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r","intervalIntegral.integral_const_mul","neg_eq_zero","nhds","rfl","sub_eq_zero_of_eq","tendsto_const_nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUShift","name":"GinibrePoincare.drivenOUPath_congr_nonneg","type_dependencies":["CompleteSpace","Eq","GinibrePoincare.drivenOUPath","LE.le","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And.intro","CompleteSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUPath","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","LE.le","Lattice.toSemilatticeInf","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instLE","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instZero","Real.lattice","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","Set.uIcc","Set.uIcc_of_le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","True","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","id","instHAdd","instHMul","instHSMul","instHSub","intervalIntegral","intervalIntegral.integral_congr","le_rfl","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOU","name":"GinibrePoincare.drivenOUPath_continuous","type_dependencies":["CompleteSpace","Continuous","GinibrePoincare.drivenOUPath","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","PseudoMetricSpace.toUniformSpace","Real","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Continuous","Continuous.add","ContinuousAt","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUCorrection_hasDerivAt","GinibrePoincare.drivenOUPath","HSMul.hSMul","HasDerivAt.continuousAt","Iff.mpr","IsTopologicalAddGroup.toContinuousAdd","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instMonoid","Real.instNeg","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","continuous_iff_continuousAt","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUProjection","name":"GinibrePoincare.drivenOUPath_continuousLinearMap","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","GinibrePoincare.drivenOUPath","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","Continuous.comp","Continuous.intervalIntegrable","Continuous.mul","Continuous.smul","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.intervalIntegral_comp_comm","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Function.comp","GinibrePoincare.drivenOUPath","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasureTheory.Measure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Pi.instMul","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.commRing","Real.continuous_exp","Real.exp","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.locallyFinite_volume","Real.measurableSpace","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toAddHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","continuous_const","continuous_id","eq_self","funext","id","instHAdd","instHMul","instHSMul","instHSub","instIsTopologicalRingReal","instPolynormableSpace","intervalIntegral","map_add","map_smul","map_sub","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUShift","name":"GinibrePoincare.drivenOUPath_initial_split","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HMul.hMul","HSMul.hSMul","Module.toDistribMulAction","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNeg","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHMul","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.trans","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUPath","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathOUShift.0.GinibrePoincare.drivenOUPath_initial_split._abel_1_1","congr","congrArg","id","instHAdd","instHMul","instHSMul","instHSub","intervalIntegral","smul_neg","smul_sub","zero_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOU","name":"GinibrePoincare.drivenOUPath_integral_equation","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSMul","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Continuous","Continuous.const_smul","Continuous.intervalIntegrable","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Function.hasSMul","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUCorrection_hasDerivAt","GinibrePoincare.drivenOUCorrection_zero","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath_continuous","HAdd.hAdd","HSMul.hSMul","HSub.hSub","IntervalIntegrable","IsBoundedSMul.toUniformContinuousConstSMul","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.lattice","Real.locallyFinite_volume","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","Set.uIcc","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathOU.0.GinibrePoincare.drivenOUPath_integral_equation._abel_1_2","congrArg","id","instHAdd","instHSMul","instHSub","intervalIntegral","intervalIntegral.integral_eq_sub_of_hasDerivAt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUQuadraticVariation","name":"GinibrePoincare.drivenOUPath_quadratic_variation_noise","type_dependencies":["Continuous","Filter.Tendsto","Filter.atTop","Finset.range","Finset.sum","GinibrePoincare.drivenOUPath","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.continuousOn","Continuous.mul","ContinuousAt","Convex.lipschitzOnWith_of_nnnorm_hasDerivWithin_le","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Eq.mp","Eq.refl","Exists","Exists.casesOn","Filter","Filter.Tendsto","Filter.atTop","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUCorrection_hasDerivAt","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath_continuous","GinibrePoincare.ginibreUniformQuadraticVariation_add_lipschitz","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","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","Or.resolve_left","Pi.instSub","Pi.smul'","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.exp_ne_zero","Real.exp_ne_zero._simp_1","Real.exp_zero","Real.instAddCommGroup","Real.instField","Real.instIsDomain","Real.instMonoid","Real.instMul","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.locallyFinite_volume","Real.measurableSpace","Real.measureSpace","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.uIcc","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathOU.0.GinibrePoincare.drivenOUPath_unique._abel_1_1","add_comm","congr","congrArg","congrFun'","continuous_const","eq_of_heq","eq_self","funext","hasDerivAt_id","id","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instHSub","instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instPolynormableSpace","intervalIntegral","intervalIntegral.integral_eq_sub_of_hasDerivAt","intervalIntegral.integral_same","intervalIntegral.integral_zero","isUnit_iff_ne_zero._simp_1","mul_neg","mul_one","neg_add_cancel","neg_smul","not_false_eq_true","of_eq_true","smul_eq_zero","smul_smul","smul_sub","smul_zero","sub_eq_zero","sub_self","sub_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUUniqueness","name":"GinibrePoincare.drivenOUPath_unique_nonneg","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","LE.le","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSMul","intervalIntegral"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And.left","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","Continuous.comp","Continuous.const_smul","Continuous.continuousOn","Continuous.integral_hasStrictDerivAt","Continuous.intervalIntegrable","Continuous.mul","Continuous.smul","Continuous.sub","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Function.comp","Function.hasSMul","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUCorrection_zero","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath.eq_1","GinibrePoincare.drivenOUPath_continuous","GinibrePoincare.drivenOUPath_integral_equation","GroupWithZero.toMonoidWithZero","GroupWithZero.toNoZeroSMulDivisors","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSMul.hSMul","HSub.hSub","HasDerivAt","HasDerivAt.congr_of_eventuallyEq","HasDerivAt.congr_simp","HasDerivAt.const_mul","HasDerivAt.exp","HasDerivAt.hasDerivWithinAt","H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.id","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SemilinearEquivClass.instSemilinearMapClass","SemilinearMapClass.toMulActionSemiHomClass","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Trans.trans","Zero.toOfNat0","commRing_strongRankCondition","congr","congrArg","congrFun","congrFun'","id","instDecidableEqFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instHSMul","instIsDomain","instLTFin","instMulZeroClassOfSemiring","instTransEq","isUnit_iff_ne_zero","map_smul","mul_comm","mul_right_cancel\u2080","smulCommClass_self","zero_ne_one"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorSpectrum","name":"GinibrePoincare.eigenpair_mem_graphOperatorSpectrum","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instNormedField","Complex.instRing","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","GinibrePoincare.graphOperatorSpectrum","HSMul.hSMul","LinearPMap","LinearPMap.graph","Membership.mem","Module.toDistribMulAction","Ne","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Complex","Complex.instNormedField","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.symm","Exists.casesOn","False","GinibrePoincare.HasBoundedGraphResolvent","HSMul.hSMul","HSub.hSub","LinearPMap","LinearPMap.graph","Membership.mem","Module.toDistribMulAction","Ne","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","instHSMul","instHSub","map_zero","sub_self"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalue","type_dependencies":["Nat","Real"],"value_dependencies":["GinibrePoincare.eigenvalueAtSpeed._proof_1","HAdd.hAdd","HMul.hMul","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAdd","Real.instMul","Real.instNatCast","instHAdd","instHMul","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalue.eq_1","type_dependencies":["Eq","GinibrePoincare.eigenvalue","GinibrePoincare.eigenvalueAtSpeed._proof_1","HAdd.hAdd","HMul.hMul","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAdd","Real.instMul","Real.instNatCast","instHAdd","instHMul","instOfNatAtLeastTwo"],"value_dependencies":["Eq.refl","GinibrePoincare.eigenvalue","Nat","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalueAtSpeed","type_dependencies":["Nat","Real"],"value_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.eigenvalueAtSpeed._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","instHAdd","instHDiv","instHMul","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalueAtSpeed._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalueAtSpeed.eq_1","type_dependencies":["DivInvMonoid.toDiv","Eq","GinibrePoincare.eigenvalueAtSpeed","GinibrePoincare.eigenvalueAtSpeed._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","instHAdd","instHDiv","instHMul","instOfNatAtLeastTwo"],"value_dependencies":["Eq.refl","GinibrePoincare.eigenvalueAtSpeed","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.eigenvalueAtSpeed_concrete","type_dependencies":["Eq","GinibrePoincare.eigenvalue","GinibrePoincare.eigenvalueAtSpeed","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.symm","Eq.trans","False","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.eigenvalueAtSpeed","GinibrePoincare.eigenvalueAtSpeed._proof_1","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InvOneClass.toOne","IsOrderedAddMonoid.toAddLeftMono","LT.lt","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast","Nat.cast_lt._simp_1","Nat.cast_zero","Not","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","True","Zero.toOfNat0","cast","congrArg","congrFun'","div_self","eq_false","eq_self","instHAdd","instHDiv","instHMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_one","ne_of_gt","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeL2Inverse","name":"GinibrePoincare.enorm_inverseVandermondeMultiplier_sq","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instNormedField","ContinuousENorm.toENorm","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instPowReal","ENorm.enorm","Eq","GinibrePoincare.Configuration","GinibrePoincare.GinibreMassIsValid","GinibrePoincare.collisionSet","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.inverseVandermondeMultiplier","GinibrePoincare.vandermondeDensity","HMul.hMul","HPow.hPow","Inv.inv","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubtractionMonoid","And.right","CommMonoid.toMonoid","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.instInv","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.nnnorm_real","Complex.normSq","Complex.normSq_eq_norm_sq","Complex.ofReal","ContinuousENorm.toENorm","DFunLike.coe","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.coe_inv","ENNReal.coe_nnreal_eq","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instPartialOrder","ENNReal.instPowReal","ENNReal.instTop","ENNReal.instZero","ENNReal.inv_pow","ENNReal.ofNNReal","ENNReal.ofReal","ENNReal.ofReal_pow","ENNReal.ofReal_toReal","ENNReal.rpow_two","ENNReal.toReal","ENNReal.toReal_nonneg","ENorm.enorm","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.Configuration","GinibrePoincare.GinibreMassIsValid","GinibrePoincare.collisionSet","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.groundStateNormalization","GinibrePoincare.inverseVandermondeMultiplier","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermonde_eq_zero_iff","HMul","HMul.hMul","HPow.hPow","Iff.mp","Inv.inv","LE.le","LT.lt","LT.lt.ne","Lattice.toSemilatticeInf","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","NNNorm.nnnorm","NNNorm.toENorm","NNReal","NNReal.instInv","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NegZeroClass.toZero","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.toNormedRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_nonneg","Real.sqrt_nonneg._simp_1","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNNNorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Set","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_eq_self._simp_1","congrArg","congrFun'","enorm_mul","eq_self","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instHPow","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_pow","nnnorm_eq_zero._simp_1","nnnorm_inv","norm_nonneg._simp_1","ofReal_norm","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingPhasePolynomial","name":"GinibrePoincare.entire_alternating_bottom_phase_is_vandermonde","type_dependencies":["AnalyticAt","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Exists","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHPow","instHSMul","instSMulOfMul"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.coeff","AddMonoidAlgebra.instDecidableEq","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AnalyticAt","And","And.casesOn","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDecidableEq","Complex.instDenselyNormedField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Eq.mpr","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.instDecidableEq","Finsupp.instFunLike","Finsupp.instZero","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternating","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.alternating_polynomial_vandermonde_division","GinibrePoincare.entire_alternating_phase_polynomial","GinibrePoincare.eval_polynomialVandermonde","GinibrePoincare.polynomialVandermonde","GinibrePoincare.quotient_eq_C_of_bottom_homogeneous_degree","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Monoid.toNPow","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MvPolynomial","MvPolynomial.C","MvPolynomial.IsHomogeneous","MvPolynomial.coeff_C","MvPolynomial.eval","MvPolynomial.eval_C","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","dite","eq_self","id","instDecidableEqFin","instDecidableEqNat","instHMul","instHPow","instHSMul","instMulZeroClassOfSemiring","instSMulOfMul","ite","ite_eq_left_of_eq_true","map_mul","map_zero","mul_comm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingPhasePolynomial","name":"GinibrePoincare.entire_alternating_phase_degree_lower_bound","type_dependencies":["AnalyticAt","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.vandermondeDegree","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NPow.toPow","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHPow","instHSMul","instLENat","instSMulOfMul"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AnalyticAt","And","And.casesOn","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Eq.mpr","Eq.refl","Exists","Exists.casesOn","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternating","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.entire_alternating_phase_polynomial","GinibrePoincare.vandermondeDegree","GinibrePoincare.vandermondeDegree_le_of_homogeneous_alternating","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.toZero","MvPolynomial","MvPolynomial.IsHomogeneous","MvPolynomial.eval","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","NonAssocSemiring.toMulZeroOneClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","instHMul","instHPow","instHSMul","instLENat","instMulZeroClassOfSemiring","instSMulOfMul","map_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingPhasePolynomial","name":"GinibrePoincare.entire_alternating_phase_polynomial","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AnalyticAt","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Exists","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAddZeroClass","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternating","GinibrePoincare.IsAlternatingConfigurationPolynomial","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.IsHomogeneous","MvPolynomial.eval","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHPow","instHSMul","instSMulOfMul"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AlgHom","AlgHom.funLike","Algebra.id","AnalyticAt","And","And.casesOn","And.intro","CharZero.infinite","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Eq.mpr","Eq.symm","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternating","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.entire_phase_has_homogeneous_mvPolynomial","GinibrePoincare.eval_permuteConfigurationPolynomial","GinibrePoincare.permutationSign","GinibrePoincare.permute","GinibrePoincare.permuteConfigurationPolynomial","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.IsHomogeneous","MvPolynomial.eval","MvPolynomial.eval_C","MvPolynomial.funext","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toNonUnitalRingHomClass","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHMul","instHPow","instHSMul","instIsDomain","instSMulOfMul","map_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EntireVandermondeFactorization","name":"GinibrePoincare.entire_alternating_vandermonde_factorization","type_dependencies":["And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Exists","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.IsSymmetric","GinibrePoincare.vandermonde","HMul.hMul","LT.lt","Nat","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.right","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.proj","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.continuous","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.decLt","Fin.fintype","Fin.instPartialOrder","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Finset.prod","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.IsSymmetric","GinibrePoincare.alternating_function_eq_zero_on_collision","GinibrePoincare.collisionLinearForm","GinibrePoincare.collisionPairs","GinibrePoincare.collisionPairs_product_eq_vandermonde","GinibrePoincare.continuous_vandermonde_quotient_symmetric","GinibrePoincare.entire_division_collisionFactors","GinibrePoincare.vandermonde","HMul.hMul","HSub.hSub","Iff.mp","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","LT.lt.ne","LinearMap","LinearMap.instFunLike","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Ne","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.module","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instContinuousSMulForall","instFintypeProd","instHMul","instHSub","instLTFin","instLTNat","instOfNatNat","instSMulOfMul","sub_eq_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryEntireCRTests","name":"GinibrePoincare.entire_compact_CR_test","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","fderiv","instHAdd","instHMul","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Bool","Bool.false","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.I","Complex.I_mul_I","Complex.SMul.instSMulRealComplex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.real_smul","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","ContDiff.differentiable","Continuous","Continuous.clm_apply","Continuous.integrable_of_hasCompactSupport","Continuous.smul","ContinuousAdd.measurableAdd","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.restrictScalars","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Differentiable","Differentiable.continuous","DifferentiableAt.fderiv_restrictScalars","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.top_ne_zero._simp_1","Eq"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ormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PathConnectedSpace.connectedSpace","Pi.instPow","PreconnectedSpace.isPreconnected_univ","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set","Set.EqOn","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.mem_univ","Set.univ","Singleton.singleton","UniformSpace.toTopologicalSpace","differentiable_id","instHMul","instHPow","instIsRCLikeNormedField","nhdsWithin"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EntireVandermondeFactorization","name":"GinibrePoincare.entire_linearDivision_preserves_hyperplane_zero","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","HMul.hMul","Nat","Ne","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Bool","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.continuous_ofReal","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDecidableEq","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.instT2Space","Complex.instZero","Complex.ofReal","Complex.ofReal_inj._simp_1","Continuous","Continuous.tendsto","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribLattice.toLattice","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.comp","Filter.Tendsto.smul_const","Filter.atTop","Filter.atTop_neBot","Filter.tendsto_atTop_add_const_right","Fin","Function.hasSMul","GinibrePoincare.Configuration","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HMul.hMul","HSMul.hSMul","Iff.mp","Inv.inv","InvOneClass.toInv","IsModuleTopology.toContinuousSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MonoidWithZero.toMulZeroOneClass","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_add._simp_1","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","One.toOfNat1","Or","Or.resolve_left","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.addZeroClass","Pi.continuousAdd'","Pi.instAdd","Pi.instZero","Pi.smulWithZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instArchimedean","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","R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module":"GinibrePoincare.Analysis.FiniteEntropyTensorization","name":"GinibrePoincare.entropy_matrix_tensorization","type_dependencies":["Finset.sum","Finset.univ","Fintype","GinibrePoincare.entropyPhi","HAdd.hAdd","LE.le","OfNat.ofNat","Real","Real.instAdd","Real.instAddCommMonoid","Real.instLE","Real.instZero","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Finset","Finset.instSetLike","Finset.mem_univ","Finset.sum","Finset.sum_comm","Finset.sum_congr","Finset.sum_const_zero","Finset.sum_eq_zero_iff_of_nonneg","Finset.sum_le_sum","Finset.sum_nonneg","Finset.sum_sub_distrib","Finset.univ","Fintype","GinibrePoincare.entropyPhi","GinibrePoincare.finite_log_sum","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Ne.symm","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.decidableEq","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.log","Real.log_zero","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.FiniteEntropyTensorization.0.GinibrePoincare.entropy_matrix_tensorization._simp_1_2","add_zero","congr","congrArg","congrFun'","dite","eq_self","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instReflLe","le_of_not_gt","lt_of_le_of_ne","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.eq_zero_of_gaussianL2FourierTest_eq_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianL2FourierTest","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.to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uilibriumFactorization","name":"GinibrePoincare.equilibriumCoordinates._proof_5","type_dependencies":["Complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instNatCast","Complex.instSemiring","DivInvMonoid.toDiv","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_recentered","GinibrePoincare.recenteredConfiguration","GinibrePoincare.zeroSumHyperplane","HAdd.hAdd","HDiv.hDiv","Membership.mem","Nat","Nat.cast","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.fst","Prod.mk","Prod.snd","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","instHAdd","instHDiv"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instNatCast","Complex.instSemiring","Complex.instSub","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_recentered","GinibrePoincare.recenteredConfiguration","GinibrePoincare.zeroSumHyperplane","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.fst","Prod.mk","Prod.snd","Ring","Ring.toAddCommGroup","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.mk","Subtype.val","Zero.toOfNat0","congrArg","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.equilibriumCoordinates_map_volume","type_dependencies":["Algebra.id","And","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofNNReal","Eq","EquivLike.toFunLike","Exists","Fin","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.configurationVolume","GinibrePoincare.equilibriumMeasurableCoordinates","GinibrePoincare.recenteredVolume","GinibrePoincare.zeroSumHyperplane","HSMul.hSMul","IsScalarTower.right","LT.lt","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.Measure.prod"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ibriumMeasurableCoordinates._proof_9","GinibrePoincare.zeroSumHyperplane","Homeomorph.toMeasurableEquiv","LT.lt","LinearEquiv.toContinuousLinearEquiv","MeasurableSpace.pi","Membership.mem","Nat","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","Prod","Prod.instAddCommGroup","Prod.instMeasurableSpace","Prod.instModule","PseudoMetricSpace.toUniformSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.instMeasurableSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.equilibriumMeasurableCoordinates._proof_1","type_dependencies":["BorelSpace","Complex","Complex.instNormedField","Complex.measurableSpace","Fin","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Fin","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.borelSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCountableFin","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.equilibriumMeasurableCoordinates._proof_10","type_dependencies":["AddCommGroup.toAddCommMonoid","Complex","Complex.addCommGroup","Complex.instField","Complex.instSemiring","DivisionRing.toRing","Field.toDivisionRing","Fin","FiniteDimensional","Nat","Pi.addCommGroup","Pi.module","Ring.toSemiring","Semiring.toModule"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.instField","Complex.instSemiring","Field.toDivisionRing","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.finiteDimensional_self","Nat","Semiring.toModule"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.equilibriumMeasurableCoordinates._proof_2","type_dependencies":["BorelSpace","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.zeroSumHyperplane","MeasurableSpace.pi","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.instMeasurableSpace","UniformSpace.toTopologicalSpace","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.zeroSumHyperplane","HereditarilyLindelof.to_Lindelof","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommMonoid","Pi.borelSpace","Pi.topologicalSpace","Prod.borelSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","SecondCountableTopology.toHereditarilyLindelof","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.borelSpace","Subtype.instMeasurableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","instCountableFin","instHereditarilyLindelofSpaceSubtype","instPseudoEMetricSpaceSubtype","instTopologicalSpaceSubtype","pseudoEMetricSpacePi","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.equilibriumMeasurableCoordinates._proof_3","type_depende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","Real.semiring","Set.Ici","Set.univ","Zero.toOfNat0","instSMulOfMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And.right","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Convex","ConvexOn","Decidable.decide","Distrib.rightDistribClass","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.le_of_le_of_eq","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast",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rmite.hermiteAntiDegreeSpan._proof_2","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_4","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_5","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.ComplexHermite.memLp_two_multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateMixedMonomialRectangleSpan","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalizedRectangleSpan","GinibrePoincare.ComplexHermite.multivariateNormalizedRectangleSpan_eq_mixedMonomialRectangleSpan","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.MemLp","MeasureTheory.MemLp.add","MeasureTheory.MemLp.const_smul","MeasureTheory.MemLp.toLp","MeasureTheory.MemLp.toLp_add","MeasureTheory.MemLp.toLp_const_smul","MeasureTheory.MemLp.zero","Membership.mem","Module.toDistribMulAction","Module.toMulActionWithZero","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulActionWithZero","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.eq_zero_of_le_zero","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instPreorder","Nat.unique_addUnits","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.instAdd","Pi.instZero","Prod","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.image","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addSubmonoidClass","Submodule.add_mem","Submodule.setLike","Submodule.smul_mem","Submodule.span","Submodule.span_induction","Submodule.subset_span","Subtype","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","Zero.toOfNat0","ZeroMemClass.zero_mem._simp_1","congrArg","congrFun'","eq_self","forall_congr","forall_const._simp_1","funext","id","implies_congr","implies_true","instHAdd","instHMul","instHPow","instHSMul","instInhabitedTrue","instLENat","instLTNat","instMulZeroOneClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","le_rfl","mul_one","of_eq_true","pow_zero","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianHermiteMoments","name":"GinibrePoincare.exists_memLp_lineMomentPolynomial_mem_gaussianHermiteSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.I","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationR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instHSub","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.fderiv_centeredObservable","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.centeredObservable","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.sub","ContinuousLinearMap.zero","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivisionRing.toRing","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.centeredObservable","GinibrePoincare.smoothGinibreMean","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun","congrFun'","differentiableAt_const","eq_self","fderiv","fderiv_fun_const","fderiv_sub","id","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","of_eq_true","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.fderiv_comp_configurationCoordinateSlice_apply","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationCoordinateSlice","GinibrePoincare.coordinateDirection","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instT2Space","Complex.instZero","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.single","ContinuousLinearMap.single_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.configurationCoordinateSlice","GinibrePoincare.coordinateDirection","GinibrePoincare.hasFDerivAt_configurationCoordinateSlice","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat","Nat.cast_one","Nat.cast_zero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.single","Pi.single_apply","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","congrFun","eq_self","fderiv","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instDecidableEqFin","instInnerProductSpaceRealComplex","instOneENat","instPolynormableSpace","instZeroENat","ite","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.fderiv_complexRadius","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.radiusBilinear","HAdd.hAdd","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommMagma.toMul","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.conjCLE","Complex.differentiable_conj","Complex.instAdd","Complex.instAddCommMonoid","Complex.in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mmMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instT2Space","ContinuousLinearMap","ContinuousLinearMap.fderiv","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","True","UniformSpace.toTopologicalSpace","congrArg","eq_self","fderiv","funext","id","instContinuousSMulForall","instInnerProductSpaceRealComplex","instPolynormableSpace","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOneParticleSpectrum","name":"GinibrePoincare.fderiv_coordinateSum_power","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNatCast","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatNat","instSubNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","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tOneENat","instPolynormableSpace","instTopologicalSpaceProd","instZeroENat","one_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDirectionalCoordinates","name":"GinibrePoincare.fderiv_ginibreDirection_decomposition","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreDirectionCoefficient","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instFintypeProd","instHMul","instInnerProductSpaceRealComplex","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRCLike","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreDirectionCoefficient","GinibrePoincare.ginibreDirection_decomposition","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Trans.trans","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fderiv","id","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatNat","instSMulOfMul","instTransEq","map_smul","map_sum","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonian","name":"GinibrePoincare.fderiv_ginibreHamiltonian_coordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instNormedField","Complex.instSub","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.erase","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.coordinateDirection","GinibrePoincare.ginibreHamiltonian","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedF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reDirectionCoefficient","GinibrePoincare.ginibreDirectionCoefficient._proof_1","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianGradientNormSq","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_im_hamiltonian","GinibrePoincare.ginibreLangevinDrift_re_hamiltonian","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instAddMonoidWithOne","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instRing","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fderiv","id","if_neg","if_true","inferInstance","instDecidableEqFin","instDecidableNot","instDecidableTrue","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","ite","ite_congr","of_decide_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonian","name":"GinibrePoincare.fderiv_ginibreHamiltonian_realCoordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configurati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inibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.coordinateDirection","GinibrePoincare.fderiv_vandermondeWeight_apply_coordinateDirection","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermondeWeight_pos_of_collisionFree","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instInv","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.log","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","eq_false","eq_self","fderiv","fderiv.log","fderiv_fun_neg","id","inferInstance","instCommCStarAlgebraComplex","instDecidableEqFin","instDistribOfSemiring","instHDiv","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsCancelMulZero","instIsTopologicalRingReal","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopENat","instZeroENat","mul_neg","mul_one","ne_of_gt","neg_mul","not_false_eq_true","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","name":"GinibrePoincare.fderiv_ginibreInteractionPotential_imaginaryCoordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","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.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instField","Real.instInv","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.log","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Ring.toAddCommGroup","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","eq_false","eq_self","fderiv","fderiv.log","fderiv_fun_neg","id","inferInstance","instCommCStarAlgebraComplex","instDistribOfSemiring","instHDiv","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsCancelMulZero","instIsTopologicalRingReal","instMulNat","instOfNat","instOfNatNat","instSMulOfMul","instTopENat","instZeroENat","mul_neg","ne_of_gt","not_false_eq_true","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","name":"GinibrePoincare.fderiv_ginibreInteractionPotential_realCoordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.realCoordinateDirection","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instInv","Complex.instNormedField","Complex.instOne","Complex.instSub","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","Eq","Eq.mpr","Eq.rec","Eq.refl","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.fderiv_ginibreInteractionPotential_coordinate","GinibrePoincare.ginibreCou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Direction","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instMulZeroClass","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instNatCast","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","congrArg","congrFun'","contDiffAt_apply","contDiffAt_prod","differentiableAt_apply","differentiableAt_pi''","fderiv","funext","id","instHMul","instHPow","instLTNat","instMulNat","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LipschitzMollification","name":"GinibrePoincare.fderiv_normed_convolution_lipschitz","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Algebra.to_smulCommClass","BorelSpace","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.normed","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.isScalarTower","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toNormedSpace._proof_1","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Eq","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LipschitzWith","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.convolution","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","NNReal","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instMonoid","Real.instMul","Real.instRCLike","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instIsTopologicalRingReal","instSMulCommClassOfIsScalarTower"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoi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CommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.instMul","Pi.instZero","Pi.single","Pi.single_apply","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","Semifield.toCommSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_mul","add_zero","congr","congrArg","congrFun","congrFun'","eq_self","fderiv","fderiv_add","fderiv_fun_const","fderiv_mul","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instSMulOfMul","ite","ite_congr","ite_eq_left_of_eq_true","ite_mul","map_add","map_mul","map_zero","mul_assoc","mul_ite","mul_one","of_eq_true","pow_one","rfl","smul_apply","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianLaplacian","name":"GinibrePoincare.fderiv_re_conj_coordinate_mul","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instStarRing","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instInnerProductSpaceRealComplex","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.conjCLE","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.mul_re","Complex.re","Complex.reCLM","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.continuousConstSMul","ContinuousLinearMap.fderiv","ContinuousLinearMap.funLike","ContinuousLinearMap.isTopologicalAddGroup","ContinuousLinearMap.module","ContinuousLinearMap.mulLeftRight","ContinuousLinearMap.proj","ContinuousLinearMap.ring","Continuo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t"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SumRadiusCoordinates","name":"GinibrePoincare.fderiv_sumRadiusPolynomial","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instStarRing","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Derivation","Derivation.instFunLike","Eq","Field.toSemifield","Fin","Fin.instOfNat","Finsupp","Finsupp.instAddCommMonoid","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.coordinateSum","GinibrePoincare.sumRadiusPolynomial","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","MulZeroClass.toZero","MvPolynomial","MvPolynomial.pderiv","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidWithOne.toAddMonoid","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Derivation","Derivation.instFunLike","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Fin.sum_univ_three","Finset.sum","Finset.univ","Finsupp","Finsupp.instAddCommMonoid","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.coordinateSum","GinibrePoincare.differentiable_sumRadiusCoordinate","GinibrePoincare.fderiv_conjugate_coordinateSum","GinibrePoincare.fderiv_coordinateSum","GinibrePoincare.fderiv_observablePolynomial","GinibrePoincare.observablePolynomial","GinibrePoincare.sumRadiusCoordinate","GinibrePoincare.sumRadiusPolynomial","GinibrePoincare.sumRadiusPolynomial.eq_1","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Matrix.vecCons","Matrix.vecEmpty","MulZeroClass.toZero","MvPolynomial","MvPolynomial.pderiv","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","add_assoc","congr","congrArg","congrFun'","eq_self","fderiv","id","instDecidableEqFin","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatNat","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.fderiv_vandermondeFactor_apply_coordinateDirection","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNeg","Complex.instNormedFi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omplexHermite.loweredCoefficients","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","name":"GinibrePoincare.finiteDbarComponentL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteDbarComponentL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteDbarComponentL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.finiteDbarComponentL2.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.loweredCoefficients","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteDbarComponentL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteDbarComponentL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.finiteDbarComponentL2_coeFn","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","Finsupp","GinibrePoincare.ComplexHermite.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atticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.pow_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","Mul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","neg_eq_zero","one_div","rfl","sub_eq_zero_of_eq"]},{"kind":"definition","module":"GinibrePoincare.Analysis.HermiteInverseSquareRoot","name":"GinibrePoincare.finiteHermiteInverseSquareRootCoefficients","type_dependencies":["Complex","Complex.instZero","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","Nat"],"value_dependencies":["Complex","Complex.instMul","Complex.instZero","Complex.ofReal","DFunLike.coe","Finsupp","Finsupp.instFunLike","Finsupp.onFinset","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.finiteHermiteInverseSquareRootCoef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inormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.finiteHomogeneousQuotientL2_coeFn","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Filter.EventuallyEq","Fin","Finset","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteHomogeneousQuotientL2","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.groundStateNormalization","GinibrePoincare.vandermonde","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","Bool","Bool.true","Classical.not_forall._simp_1","Classical.not_imp._simp_1","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","Decidab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"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSpectralContraction","name":"GinibrePoincare.finitePolynomialSpectralEvolution_hasDerivAt","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Finset","Finset.sum","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.finitePolynomialSpectralEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunctionL2","HMul.hMul","HSMul.hSMul","HasDerivAt","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","Membership.mem","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.exp","Real.instMul","Real.instNeg","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLENat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.exp","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_exp","Complex.ofReal_mul","Complex.ofReal_neg","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Finset","Finset.instSetLike","Finset.sum","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.finitePolynomialSpectralEvolution","GinibrePoincare.finitePolynomialSpectralEvolution._proof_1","GinibrePoincare.finitePolynomialSpectralEvolution._proof_2","GinibrePoincare.finitePolynomialSpectralEvolution._proof_5","GinibrePoincare.finitePolynomialSpectralEvolution._proof_6","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunctionL2","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HasDerivAt","HasDerivAt.const_mul","HasDerivAt.exp","HasDerivAt.fun_sum","HasDerivAt.ofReal_comp","HasDerivAt.smul_const","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.exp","Real.instMul","Real.instNeg","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TopologicalSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_of_heq","eq_self","fact_one_le_two_ennreal","hasDerivAt_id","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLENat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","mul_one","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticFiniteKernelIntegral","name":"GinibrePoincare.finit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ePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.finiteZeroHermiteL2_coeFn","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","Finset","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EmptyCollection.emptyCollection","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finset","Finset.induction_on","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.sum","Finset.sum_insert","Fintype.decidablePiFintype","Function.hasSMul","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family_coeFn","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.finiteZeroHermiteL2._proof_1","GinibrePoincare.gaussianGlobalPhaseL2._proof_1","GinibrePoincare.gaussianGlobalPhaseL2._proof_2","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_1","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_2","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_4","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Insert.insert","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_add","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.coeFn_zero","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","Pi.instAdd","Pi.instZero","Pi.zero_apply","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","id","instDecidableEqNat","instHAdd","instHMul","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.finiteZeroHermiteL2_mem_antiDegreeZeroSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Finset","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteZeroHermiteL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.refl","Eq.trans","Exists.intro","Field.toDivisionRing","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_eq_zero_iff._simp_1","Finset.univ","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_1","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_2","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_4","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_5","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.finiteZeroHermiteL2._proof_1","GinibrePoincare.gaussianGlobalPhaseL2._proof_1","GinibrePoincare.gaussianGlobalPhaseL2._proof_2","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_1","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.unique_addUnits","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instZero","Prod","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.image","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.smul_mem","Submodule.subset_span","Submodule.sum_mem","Subtype","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","Zero.toOfNat0","congrArg","congrFun'","eq_self","forall_congr","forall_const._simp_1","funext","id","implies_congr","implies_true","instHSMul","instInhabitedTrue","instLTNat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.finiteZeroHermiteL2_mem_gaussianAlternating","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Finset","GinibrePoincare.Configuration","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.gaussianAlternatingL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Finset","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteHermiteSum_isAlternating_iff","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.finiteZeroHermiteL2_coeFn","GinibrePoincare.gaussianAlternatingL2._proof_4","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.gaussianPermutationL2._proof_1","GinibrePoincare.gaussianPermutationL2._proof_2","GinibrePoincare.gaussianSymmetricL2._proof_4","GinibrePoincare.gaussianSymmetricL2._proof_5","GinibrePoincare.gaussian_measurePreserving_permute","GinibrePoincare.permutationSign","GinibrePoincare.permute","HMul.hMul","HSMul.hSMul","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHMul","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.finite_bottom_quotient_generator_ae_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsFiniteHomogeneousQuotientVector","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddComm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_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","neg_eq_zero","rfl","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryFirstModeSeries","name":"GinibrePoincare.firstModeHermite_series_creation","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instInv","Complex.instMul","Complex.instNorm","Complex.instNormedField","Complex.instStarRing","Complex.instSub","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","GinibrePoincare.realCoordinateDirection","HMul.hMul","HSub.hSub","Inv.inv","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.cast","Nat.instMulZeroClass","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instNatCast","Real.sqrt","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHMul","instHSub","instLTNat","instOfNatNat","starRingEnd","tsum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.instT2Space","Complex.instZero","Complex.ofReal","Complex.ofReal_mul","Complex.ofReal_ne_zero","ContDiffAt.differentiableAt_one","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.map_tsum","ContinuousLinearMap.module","ContinuousLinearMap.smul_apply","ContinuousLinearMap.topologicalSpace","DFunLike.coe","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.const_mul","DifferentiableAt.fun_comp'","DifferentiableAt.fun_pow","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","Div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Field","Complex.instInv","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.instZero","Complex.ofReal","Complex.ofReal_mul","Complex.ofReal_ne_zero","ContDiffAt.differentiableAt_one","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","DFunLike.coe","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.const_mul","DifferentiableAt.fun_comp'","DifferentiableAt.fun_pow","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized_zero_right","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","GinibrePoincare.fderiv_holomorphicHermite_coordinate","GinibrePoincare.gaussianHermite_firstMode_creation","GinibrePoincare.realCoordinateDirection","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_mul","Nat.cast_nonneg","Nat.cast_pos","Nat.instMulZeroClass","Ne","NeZero.one","Neg.neg","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instIsOrderedRing","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instZero","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_mul","Real.sqrt_pos","Ring.toAddCommGroup","Ring.toNonAssocRing","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoM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omplex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.fullNoiseMeasurable","MeasurableSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltCanonicalMap","name":"GinibrePoincare.fullNoiseMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","borel","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.FullNonQuadraticPotential","name":"GinibrePoincare.fullNonQuadraticPotentialTheorem","type_dependencies":["GinibrePoincare.NonQuadraticPotentialTheorem","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["CommMagma.toMul","CommRing.toNonUnitalCommRing","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq.mp","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRadialFunctionLSI","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.NonQuadraticPotentialTheorem.mk","GinibrePoincare.Potential","GinibrePoincare.bakryEmery_potential_smooth_radial_lsi","GinibrePoincare.potentialGradientEnergy","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.rhoSubharmonic_potential_smooth_poincare","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Top.top","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","congrFun'","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","mul_comm"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.FullTheoremOneNine","name":"GinibrePoincare.fullTheoremOneNine","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullCenteredTransform","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.modeTail","GinibrePoincare.positiveHermiteModeMass","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","Subtype.val","Summable","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","And.casesOn","And.intro","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLin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ormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Decidable.decide","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.GinibreGeneratorDeficits","GinibrePoincare.GinibreGeneratorDeficits.distributional_gradient","GinibrePoincare.GinibreGeneratorDeficits.equality_iff_affine","GinibrePoincare.GinibreGeneratorDeficits.generator_deficit","GinibrePoincare.GinibreGeneratorDeficits.poincare_deficit","GinibrePoincare.GinibreGeneratorDeficits.symmetric_gradient","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.coordinateSum","GinibrePoincare.fullTheoremOneNine_named","GinibrePoincare.ginibreDifferentialDeficitVector","GinibrePoincare.ginibreDifferentialDeficit_weak_derivatives","GinibrePoincare.ginibreDifferentialFirstDerivative","GinibrePoincare.ginibreDifferentialSecondDerivative","GinibrePoincare.ginibreDifferentialSecondEnergy","GinibrePoincare.ginibreDifferentialSecondEnergy_eq_tail","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullCenteredTransform","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.modeTail","GinibrePoincare.positiveHermiteModeMass","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","LinearPMap.graph","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Ne","NeZero.one","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing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mplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGaussianSchwartzDbar","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.coordinateSum","GinibrePoincare.fullTheoremOneTen_named","GinibrePoincare.gaussianSchwartzDbar_iff_weak","GinibrePoincare.ginibreDifferentialDeficitVector","GinibrePoincare.ginibreDifferentialFirstDerivative","GinibrePoincare.ginibreDifferentialSecondDerivative","GinibrePoincare.ginibreDifferentialSecondEnergy","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.ginibreWeakEnergy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff","Iff.mpr","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.FullTheoremOneTen","name":"GinibrePoincare.fullTheoremOneTen_named","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.a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.id","RingHomInvPair","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RingHomInvPair.ids","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormCoefficients","name":"GinibrePoincare.gaussianClosedFormPotential._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.ComplexHermite.HermiteMultiIndex","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","RCLike.toDenselyNormedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instRCLike","DenselyNormedField.toNormedField","GinibrePoincare.ComplexHermite.HermiteMultiIndex","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","RCLike.toDenselyNormedField","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormCoefficients","name":"GinibrePoincare.gaussianClosedFormPotential.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianClosedFormPotential","GinibrePoincare.gaussianClosedFormPotential._proof_1","GinibrePoincare.gaussianClosedFormPotential._proof_2","GinibrePoincare.gaussianClosedFormPotentialCoefficient._proof_1","GinibrePoincare.gaussianClosedFormPotentialCoefficient._proof_2","GinibrePoincare.gaussianClosedFormPotentialCoefficients","GinibrePoincare.gaussianHermiteHilbertBasis","HilbertBasis.repr","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PreLp","PreLp.instAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","lp","lp.instModuleSubtypePreLpMemAddSubgroup","lp.normedAddCommGroup"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure",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Poincare.gaussianEntireClosedSpace._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireSpaceClosure","name":"GinibrePoincare.gaussianEntireClosedSpace.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireClosedSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireClosedSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologic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roup","AddSubgroup.instSetLike","Complex","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianEntireRepresentative","GinibrePoincare.complexGaussianMeasure","HMul.hMul","HPow.hPow","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instZero","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","tsum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","And.left","And.right","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.continuous","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.symm","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianEntireRepresentative","GinibrePoincare.IsGaussianEntireRepresentative._proof_2","GinibrePoincare.IsGaussianEntireRepresentative._proof_3","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","GinibrePoincare.differentiable_holomorphicHermite_series","GinibrePoincare.gaussianEntireRepresentative_zeroMode_eq","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_norm_le","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianZeroMode_holomorphic_series_ae","GinibrePoincare.norm_holomorphicHermite_le_tensor_bound","GinibrePoincare.summable_holomorphicHermite_series","GinibrePoincare.summable_tensor_holomorphicHermite_bound","HMul.hMul","HPow.hPow","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminorm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ormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.continuous","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianEntireRepresentative","GinibrePoincare.IsGaussianEntireRepresentative._proof_2","GinibrePoincare.IsGaussianEntireRepresentative._proof_3","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.continuousAdd'","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instContinuousSMulForall","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireSpaceClosure","name":"GinibrePoincare.gaussianEntireRepresentative_zeroMode_eq","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianEntireRepresentative","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","And.left","And.right","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianEntireRepresentative","GinibrePoincare.IsGaussianEntireRepresentative._proof_2","GinibrePoincare.IsGaussianEntireRepresentative._proof_3","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent_eq_zero_of_differentiable_complex","GinibrePoincare.gaussianWeakDbar_zero_modeZero","GinibrePoincare.gaussian_entire_contDiff_real_one","GinibrePoincare.gaussian_smooth_weak_dbar","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","Measu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l"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltMoments","name":"GinibrePoincare.gaussianExponentialTilt_integrable","type_dependencies":["GinibrePoincare.gaussianExponentialTilt","MeasureTheory.Integrable","NNReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianExponentialTilt.eq_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Integrable","MeasureTheory.Integrable.const_mul","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.gaussianReal","ProbabilityTheory.integrable_exp_mul_gaussianReal","PseudoMetricSpace.toUniformSpace","Rat.rawCast","Real","Real.commRing","Real.exp","Real.exp_add","Real.instAdd","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltMoments","name":"GinibrePoincare.gaussianExponentialTilt_integral","type_dependencies":["Eq","GinibrePoincare.gaussianExponentialTilt","InnerProductSpace.toNormedSpace","MeasureTheory.integral","NNReal","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","RCLike.toInnerProductSpaceReal","Real","Real.instOne","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Zero.toOfNat0"],"value_dependencies":["AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.trans","Field.toSemifield","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt_exponential_moment","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.integral","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.exp_zero","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.semiring","Semifield.toDivisionSemiring","SubNegMonoid.toAddMonoid","Zero.toOfNat0","congr","congrArg","congrFun'","funext","id","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","one_mul","one_pow","sub_self","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltMoments","name":"GinibrePoincare.gaussianExponentialTilt_integral_sq","type_dependencies":["Eq","GinibrePoincare.gaussianExponentialTilt","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.gaussianReal","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Zero.toOfNat0","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianExponentialTilt.eq_1","GinibrePoincare.gaussianExponentialTilt_exponential_moment","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","M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odule","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.seminormedAddCommGroup","Pi.single","Pi.single_apply","Pi.topologicalSpace","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.log","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomCompTriple.ids","RingHomInvPair.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GaussianFiniteIndexLSI.0.GinibrePoincare.gaussianFiniteIndex_lsi_compactLipschitz._simp_1_2","congr","congrArg","congrFun'","eq_rec_constant","eq_self","fderiv","funext","id","instAddNat","instCountableFin","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","ite","ite_congr","locallyCompact_of_proper","measurable_fderiv_apply_const","of_eq_true","pseudoEMetricSpacePi","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormCurl","name":"GinibrePoincare.gaussianForm_potentialCoefficient_of_coefficientCurl","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianClosedFormPotential","GinibrePoincare.gaussianHermiteCoefficient","HAdd.hAdd","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.sqrt","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_mul","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","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.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianGlobalPhaseL2","GinibrePoincare.globalPhase","GinibrePoincare.measurePreserving_globalPhase_complexGaussianMeasure","GinibrePoincare.multivariateNormalized_globalPhase","GinibrePoincare.totalHolomorphicDegree","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHMul","instHPow","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.gaussianGlobalPhaseL2_hermite_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteL2Family","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianGlobalPhaseL2","GinibrePoincare.totalHolomorphicDegree","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUn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ormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHPow","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset.Ioi","Finset.card","Finset.sum","Finset.univ","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianMeasure_absolutelyContinuous_ginibreMeasure","GinibrePoincare.gaussianGlobalPhaseL2","GinibrePoincare.ginibreGlobalPhaseL2","GinibrePoincare.ginibreMassEvaluation","GinibrePoincare.ginibreMeasure","GinibrePoincare.globalPhase","GinibrePoincare.groundStateNormalization","GinibrePoincare.measurePreserving_globalPhase_complexGaussianMeasure","GinibrePoincare.measurePreserving_globalPhase_ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_coeFn_public","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","GinibrePoincare.vandermondeDegree_eq_sum_Ioi_card","GinibrePoincare.vandermonde_globalPhase","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid"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rePoincare.gaussianHermiteFirstLoweringTerm._proof_4","GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_5","GinibrePoincare.multivariateNormalizedL2","HMul.hMul","HSMul.hSMul","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.sqrt","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instHSMul","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","name":"GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","name":"GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","name":"GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_3","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","name":"GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteFirstLoweringTerm._proof_1","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalS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roup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.gaussianHermiteCoefficient_ext","GinibrePoincare.gaussianHermiteCoefficient_inverseSquareRoot","GinibrePoincare.gaussianHermiteInverseSquareRoot","GinibrePoincare.hermiteInverseSquareRootWeight","GinibrePoincare.multivariateNormalizedL2","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","eq_self","fact_one_le_two_ennreal","id","inner_smul_right","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteInverseSquareRoot","name":"GinibrePoincare.gaussianHermiteInverseSquareRootCLM._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Nor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oMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","lp","lp.instModuleSubtypePreLpMemAddSubgroup","lp.normedAddCommGroup"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","Complex.norm_real","Complex.ofReal","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","EquivLike.toFunLike","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteHilbertBasis","GinibrePoincare.hermiteInverseSquareRootWeight","GinibrePoincare.hermiteInverseSquareRootWeight_le_one","GinibrePoincare.hermiteInverseSquareRootWeight_nonneg","HMul.hMul","HilbertBasis.repr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","LE.le","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PreLp","PreLp.instAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.partialOrder","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","abs","abs_of_nonneg","congrArg","fact_one_le_two_ennreal","id","instHMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","lp","lp.instModuleSubtypePreLpMemAddSubgroup","lp.normedAddCommGroup","mul_le_of_le_one_left","norm_mul","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteInverseSquareRoot","name":"GinibrePoincare.gaussianHermiteInverseSquareRootCoefficients._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteInverseSquareRoot","name":"GinibrePoincare.gaussianHermiteInverseSquareRootCoefficients._proof_3","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteInverseSquareRoot","name":"GinibrePoincare.gaussianHermiteInverseSquareRootCoefficients._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoi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roup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianHermiteMode","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianAlternatingL2._proof_4","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianHermiteMode_eq_antiDegreeProjection","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.gaussianPermutationL2._proof_1","GinibrePoincare.gaussianPermutationL2._proof_2","GinibrePoincare.gaussianPermutationL2_comm_gaussianHermiteMode","GinibrePoincare.gaussianSymmetricL2._proof_4","GinibrePoincare.gaussianSymmetricL2._proof_5","GinibrePoincare.permutationSign","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing"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Poincare.gaussianHermiteModeTerm._proof_2","GinibrePoincare.gaussianHermiteModeTerm._proof_3","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.summable_gaussianHermiteModeTerm","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsClosed.mem_of_tendsto","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.smul_mem","Submodule.sum_mem","Submodule.toAddSubmonoid","Submodule.zero_mem","Subtype","Summable.hasSum","SummationFilter.filter","SummationFilter.instNeBotFinsetFilterOfNeBot","SummationFilter.instNeBotUnconditional","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","dite","fact_one_le_two_ennreal","id","instDecidableEqNat","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_left","ite_eq_right","tsum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.WeightedSeriesTruncation","name":"GinibrePoincare.gaussianHermiteMode_partialSum_eq_zero_of_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianHermiteModePartialSum","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.sum","Finset.sum_eq_zero","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.HermiteWeightedDomain._proof_1","GinibrePoincare.HermiteWeightedDomain._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianHermiteModePartialSum","GinibrePoincare.gaussianHermiteModePartialSum._proof_1","GinibrePoincare.gaussianHermiteModePartialSum._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ologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialDensity","name":"GinibrePoincare.gaussianHermiteSpan._proof_2","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialDensity","name":"GinibrePoincare.gaussianHermiteSpan._proof_3","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialDensity","name":"GinibrePoincare.gaussianHermiteSpan._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteSpan._proof_1","GinibrePoincare.gaussianHermiteSpan._proof_3","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialDensity","name":"GinibrePoincare.gaussianHermiteSpan._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","Ne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CommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.gaussianHermiteSpan_orthogonal_eq_bot","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Bot.bot","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteSpan","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Submodule","Submodule.instBot","Submodule.orthogonal","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","Bot.bot","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.eq_zero_of_orthogonal_hermites","GinibrePoincare.gaussianHermiteSpan","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.multivariateNormalizedL2_mem_span","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Submodule","Submodule.eq_bot_iff","Submodule.instBot","Submodule.orthogonal","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instLTNat","instOfNatAtLeastTwo","instOfNatNat","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.gaussianHermiteSpan_topologicalClosure_eq_top","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussian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ianHermite_coordinate_creation_pointwise","type_dependencies":["Complex","Complex.instAdd","Complex.instMul","Complex.instNatCast","Complex.ofReal","Eq","Fin","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","HAdd.hAdd","HMul.hMul","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instNatCast","Real.sqrt","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["Complex","Complex.instAdd","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.ofReal","ContDiff.continuous","Continuous.add","Continuous.mul","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","GinibrePoincare.contDiff_multivariateNormalized_real","GinibrePoincare.continuous_eq_of_ae_eq_complexGaussian","GinibrePoincare.coordinate_mul_multivariateNormalized_creation_ae","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instNatCast","Real.instRCLike","Real.sqrt","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","congrFun","continuous_apply","continuous_const","instAddNat","instHAdd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instMulNat","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFirstModeCreation","name":"GinibrePoincare.gaussianHermite_firstMode_creation","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instStarRing","Complex.instSub","Complex.ofReal","DFunLike.coe","Eq","Fin","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","HMul.hMul","HSub.hSub","LT.lt","MulZeroClass.toZero","Nat","Nat.cast","Nat.instMulZeroClass","OfNat.ofNat","Pi.instZero","Real","Real.instNatCast","Real.sqrt","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHMul","instHSub","instLTNat","instOfNatNat","starRingEnd"],"value_dependencies":["AddCancelMonoid.toAddRightCancelMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddRightCancelMonoid.toAddRightCancelSemigroup","AddRightCancelSemigroup.toIsRightCancelAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toModule","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.conj_natCast","Complex.conj_ofReal","Complex.instAdd","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.instZero","Complex.ofReal","Complex.ofReal_inj._simp_1","Complex.ofReal_mul","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.lowerAt","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseAt","GinibrePoincare.Configuration","GinibrePoincare.conj_multivariateNormalized_swap","GinibrePoincare.gaussianHermite_coordinate_creation_pointwise","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub"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ormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_1","GinibrePoincare.gaussianHolomorphicDegreeSpan._proof_3","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.gaussianHolomorphicDegreeSpan.match_1","type_dependencies":["Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","Nat","Prod.mk"],"value_dependencies":["Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","Nat","Prod.casesOn","Prod.mk"]},{"kind":"definition","module":"GinibrePoincare.Concrete.Wirtinger","name":"GinibrePoincare.gaussianHolomorphicDistanceSq","type_dependencies":["Complex","GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["Complex","GinibrePoincare.Configuration","GinibrePoincare.gaussianHolomorphicErrors","InfSet.sInf","Nat","Real","Real.instInfSet"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDistance","name":"GinibrePoincare.gaussianHolomorphicDistanceSq_eq_projectionNorm","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireClosedSpace","GinibrePoincare.gaussianHolomorphicDistanceSq","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCom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oid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GaussianEntireDistance.0.GinibrePoincare.gaussianHolomorphicDistanceSq_eq_projectionNorm._abel_1_1","congr","congrArg","csInf_le","fact_one_le_two_ennreal","id","inferInstance","instClosedIciTopology","instContinuousSMulForall","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","le_antisymm","le_csInf","le_of_not_gt","lowerBounds","mul_self_nonneg","neg_eq_zero","norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero","pow_two","rfl","sub_eq_zero_of_eq"]},{"kind":"definition","module":"GinibrePoincare.Concrete.Wirtinger","name":"GinibrePoincare.gaussianHolomorphicErrors","type_dependencies":["Complex","GinibrePoincare.Configuration","Nat","Real","Set"],"value_dependencies":["And","Complex","Eq","Exists","GinibrePoincare.Configuration","GinibrePoincare.IsEntire","GinibrePoincare.IsGaussianL2","GinibrePoincare.gaussianComplexError","Nat","Real","Set.ofPred"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.gaussianImagPartNegativeMeasure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.im","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_1","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_2","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure.withDensity","Membership.mem","Nat","Neg.neg","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMax","Real.instNeg","Real.instZero","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.gaussianImagPartPositiveMeasure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.im","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_1","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_2","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4"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NonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivInvMonoid.toInv","DivInvMonoid.toMonoid","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv.Perm.instInv","Equiv.Perm.instMul","Equiv.Perm.instOne","Equiv.Perm.permGroup","Equiv.symm","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.gaussianPermutationL2_comp_apply","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.gaussianPermutationL2_mem_antiDegreeClosedSpan","Group.toDivInvMonoid","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.map_starProjection","LinearIsometry.toLinearMap","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","RingHomSurjective.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Submodule","Submodule.HasOrthogonalProjection","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.instPartialOrder","Submodule.map","Submodule.setLike","Submodule.starProjection","Submodule.starProjection.congr_simp","Subtype","Trans.trans","True","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.HermiteParsevalModes.0.GinibrePoincare.gaussianPermutationL2_one","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","inferInstance","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTransEq","le_antisymm","mul_inv_cancel","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteParsevalModes","name":"GinibrePoincare.gaussianPermutationL2_comm_gaussianHermiteMode","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianPermutationL2","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianHermiteMode_eq_antiDegreeProjection","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.gaussianPermutationL2_comm_antiDegreeProjection","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HermiteParsevalModes","name":"GinibrePoincare.gaussianPermutationL2_mem_antiDegreeClosedSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid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HermiteParsevalModes","name":"GinibrePoincare.gaussianPermutationL2_multivariateNormalizedL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.multivariateNormalizedL2","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Fin","GinibrePoincare.ComplexHermite.gaussianPermutationL2_hermiteL2Family","GinibrePoincare.ParticlePermutation","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianPiCoordinates","name":"GinibrePoincare.gaussianPiEnergy","type_dependencies":["Fin","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.single","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instOne","Real.instRing","Real.instZero","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instDecidableEqFin","instHPow","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFiniteIndexBoundedLSI","name":"GinibrePoincare.gaussianPi_lsi_bounded_C1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.gaussianPiEnergy","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.Measure.pi","MeasureTheory.integral","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instLE","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","abs","fderiv","instAddNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMono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opologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurableDiv_of_mul_inv","measurable_id'","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltPredictable","name":"GinibrePoincare.gaussianPredictableTilt_lintegral_sq","type_dependencies":["AEMeasurable","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","GinibrePoincare.gaussianExponentialTilt","HMul.hMul","HPow.hPow","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.lintegral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instZero","Real.measurableSpace","Semiring.toMonoid","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AEMeasurable","AEMeasurable.ennreal_ofReal","AEMeasurable.exp","AEMeasurable.fun_mul","AEMeasurable.mul_const","AEMeasurable.pow_const","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub\u2082","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instMeasurableMul\u2082","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mp","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianExponentialTilt_product_lintegral_sq","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.aemeasurable","Measurable.div_const","Measurable.ennreal_ofReal","Measurable.exp","Measurable.fst","Measurable.fun_comp","Measurable.fun_mul","Measurable.fun_sub","Measurable.mul_const","Measurable.pow_const","Measurable.snd","MeasurableSpace","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instSFiniteMap","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.lintegral","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instMeasurableSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.lintegral_comp","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.hasLaw_prod","ProbabilityTheory.gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Semifield.toDivisionSemiring","Semiring.toMonoid","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurableDiv_of_mul_inv","measurable_id'","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUFiniteLaw","name":"GinibrePoincare.gaussianProcess_finite_euclidean_hasGaussianLaw","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fintype","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Pi.Function.module","Pi.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oid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.finrank_real_complex","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","Fin.sum_univ_eq_sum_range","Fin.val","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","Finset","Finset.card","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.sum_range_succ","Finset.univ","Fintype.card_fin","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Module.Free.function","Module.Free.of_divisionRing","Module.finrank","Module.finrank_pi_fintype","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","NSMul.toSMul","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instAddMonoidWithOne","Nat.instCommSemiring","Nat.instMulOneClass","Nat.rawCast","Nat.recAux","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.module","Real","Real.commRing","Real.instDivisionRing","Real.instNontrivial","Real.instRCLike","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","Zero.toOfNat0","commRing_strongRankCondition","congrArg","congrFun'","eq_self","id","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","mul_comm","mul_one","of_eq_true","rfl","zero_add"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GaussianFourierUniqueness","name":"GinibrePoincare.gaussianRealPartNegativeMeasure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.re","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_1","GinibrePoincare.gaussianRealPartPositiveMeasure._proof_2","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure.withDensity","Membership.mem","Nat","Neg.neg","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUnifor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ibrePoincare.gaussianReal_lsi_variance","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","deriv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","DistribLattice.toLattice","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.gaussianReal_lsi_dilation","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","MeasureTheory.Measure","MeasureTheory.Measure.dirac","MeasureTheory.integral","MeasureTheory.integral_dirac","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","NNReal","NNReal.coe_lt_coe._simp_1","NNReal.coe_nonneg","NNReal.instLinearOrder","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_zero_var","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.log","Real.log_pow","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_pos","Ring.toAddGroupWithOne","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StandardBorelSpace.instMeasurableEq","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","Subtype","Subtype.ext","Subtype.mk","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","cast","congr","congrArg","congrFun'","deriv","dite","funext","instDistribLatticeOfLinearOrder","instHMul","instHPow","instHSub","instMeasurableSingletonClassOfMeasurableEq","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instReflLe","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","of_eq_true","pos_iff_ne_zero","sq_nonneg","standardBorel_of_polish","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIScaling","name":"GinibrePoincare.gaussianReal_lsi_variance_C1","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Field.toSemifi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CompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurable_id'","neg_mul","of_eq_true","sub_eq_add_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIProduct","name":"GinibrePoincare.gaussianReal_prod_lsi_C1","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.gaussianPartialLeft","GinibrePoincare.gaussianPartialRight","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.Measure.prod","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","Prod","Prod.instMeasurableSpace","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","ContinuousLinearMap","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","ENat","Exists","Exists.casesOn","Field.toSemifield","GinibrePoincare.gaussianPartialLeft","GinibrePoincare.gaussianPartialRight","GinibrePoincare.gaussianReal_prod_lsi_bounded_C1","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.exists_bound_of_continuous","HasCompactSupport.fderiv","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","LE.le","LE.le.trans","MeasureTheory.Measure.prod","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","Prod","Prod.instAddCommGroup","Prod.instMeasurableSpace","Prod.instModule","Prod.normedAddCommGroup","Prod.normedSpace","Prod.seminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","abs","abs_nonneg","fderiv","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instTopologicalSpaceProd","instZeroENat","le_abs_self","one_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIProduct","name":"GinibrePoincare.gaussianReal_prod_lsi_bounded_C1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","GinibrePoincare.gaussianPartialLeft","GinibrePoincare.gaussianPartialRight","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.Measure.prod","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","Prod","Prod.instAddCommGroup","Prod.instMeasurableSpace","Pr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oEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","Zero.toOfNat0","abs","congrArg","deriv","div_le_self","id","inferInstance","instCountableFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instPreorderENat","instT6SpaceOfMetrizableSpace","instTopENat","le_of_not_gt","mul_le_mul_of_nonneg_right","norm_mul","norm_nonneg","not_false_eq_true","of_eq_true","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarCompactCore","name":"GinibrePoincare.gaussianSpatialCutoff_derivativeTerm_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianSpatialCutoff_derivativeTerm_memLp","GinibrePoincare.sobolevCutoff","HMul.hMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","fact_one_le_two_ennreal","instHMul","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instAddMonoidHomClass","AddMonoidHom.instFunLike","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.to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brePoincare.Analysis.PermutationLp","name":"GinibrePoincare.gaussianSymmetricL2._proof_4","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PermutationLp","name":"GinibrePoincare.gaussianSymmetricL2._proof_5","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PermutationLp","name":"GinibrePoincare.gaussianSymmetricL2._proof_6","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PermutationLp","name":"GinibrePoincare.gaussianSymmetricL2._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianSymmetricL2._proof_4","GinibrePoincare.gaussianSymmetricL2._proof_6","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector","name":"GinibrePoincare.gaussianVectorExponentialTilt","type_dependencies":["Fintype","NNReal","Real"],"value_dependencies":["Finset.prod","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","NNReal","Real","Real.instCommMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector","name":"GinibrePoincare.gaussianVectorExponentialTilt.eq_1","type_dependencies":["Eq","Finset.prod","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianVectorExponentialTilt","NNReal","Real","Real.instCommMonoid"],"value_dependencies":["Eq.refl","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVectorCentering","name":"GinibrePoincare.gaussianVectorExponentialTilt_centered_lintegral","type_dependencies":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HMul.hMul","HSub.hSub","Measurable","MeasurableSpace.pi","MeasureTheory.Measure.pi","MeasureTheory.lintegral","NNReal","NNReal.toReal","OfNat.ofNat","ProbabilityTheory.gaussianReal","Real","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHSub"],"value_dependencies":["CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousMul.measurableMul","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mp","Eq.symm","Finset","Finset.instSetLike","Finset.measurable_prod","Finset.prod","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianReal_pi_exponential_tilt_centered","GinibrePoincare.gaussianVectorExponentialTilt","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.const_mul","Measurable.ennreal_ofReal","Measurable.exp","Measurable.fun_comp","Measurable.of_eval","Measurable.sub_const","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","MeasureTheory.lintegral","MeasureTheory.lintegral_map","MeasureTheory.lintegral_withDensity_eq_lintegral_mul","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","Pi.instMul","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddGroup","Real.instCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","measurable_pi_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector","name":"GinibrePoincare.gaussianVectorExponentialTilt_eq_exp","type_dependencies":["DivInvMonoid.toDiv","Eq","Finset.sum","Finset.univ","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["DivInvMonoid.toDiv","Eq","Eq.trans","Finset.prod","Finset.sum","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt._proof_1","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.exp","Real.exp_sum","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","True","congrArg","eq_self","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector","name":"GinibrePoincare.gaussianVectorExponentialTilt_integrable","type_dependencies":["F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rib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Finset.sum","Finset.univ","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HMul.hMul","HPow.hPow","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.Measure.prod","MeasureTheory.SFinite","MeasureTheory.lintegral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","ProbabilityTheory.gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","Real","Real.exp","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instZero","Real.measurableSpace","Semiring.toMonoid","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AEMeasurable","AEMeasurable.div_const","AEMeasurable.ennreal_ofReal","AEMeasurable.exp","AEMeasurable.fst","AEMeasurable.fun_mul","AEMeasurable.fun_sub","AEMeasurable.mul_const","AEMeasurable.pow_const","AEMeasurable.snd","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub","ContinuousSub.measurableSub\u2082","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instMeasurableMul\u2082","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mpr","Eq.rec","Eq.refl","Field.toSemifield","Finset","Finset.aemeasurable_fun_prod","Finset.instSetLike","Finset.measurable_prod","Finset.prod","Finset.sum","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianVectorExponentialTilt","GinibrePoincare.gaussianVectorExponentialTilt_lintegral_sq","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.comp_aemeasurable'","Measurable.const_mul","Measurable.ennreal_ofReal","Measurable.exp","Measurable.fun_comp","Measurable.pow_const","Measurable.sub_const","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.SFinite","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.lintegral","MeasureTheory.lintegral_const_mul","MeasureTheory.lintegral_prod","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instMeasurableSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Semifield.toDivisionSemiring","Semiring.toMonoid","SetLike.instMembership","T5Space.toT1Space","T6Space.toT0Space","T6Space.toT5Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_id","congrArg","funext","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableDiv_of_mul_inv","measurable_pi_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector","name":"GinibrePoincare.gaussianVectorExponentialTilt_sq_integrable","type_dependencies":["Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HPow.hPow","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure.pi","Monoid.toNPow","NNReal","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instZero","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatNat"],"value_dependencies":["CommMonoid.toMonoid","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Finset.prod","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt_sq_integrable","GinibrePoincare.gaussianVectorExponentialTilt","HPow.hPow","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.fintype_prod_dep","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.pi","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instCommMonoid","Real.instCompleteSpace","Real.instMonoid","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.BrownianIntegralGaussianTiltVector.0.GinibrePoincare.gaussianVectorExponentialTilt_sq_integrable._simp_1_2","autoParam","congrArg","congrFun'","funext","id","instHPow","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltFreshLaw","name":"GinibrePoincare.gaussianVectorPredictableTilt_centered_fresh","type_dependencies":["And","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instOne","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HMul.hMul","HSub.hSub","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","MeasureTheory.lintegral","NNReal","NNReal.toReal","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","Real","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHSub"],"value_dependencies":["AEMeasurable.fst","AEMeasurable.snd","Algebra.id","And","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","DFunLike.coe","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instOne","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mpr","Eq.trans","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","GinibrePoincare.gaussianVectorPredictableTilt_centered_map","GinibrePoincare.gaussianVectorPredictableTilt_lintegral","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mpr","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","Measurable","Measurable.aemeasurable","Measurable.fun_comp","Measurable.fun_sub","Measurable.mul_const","Measurable.of_eval","Measurable.prodMk","MeasurableSet.univ","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsProbabilityMeasure.measure_univ","MeasureTheory.IsProbabilityMeasure.mk","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.Measure.map_fst_prod","MeasureTheory.Measure.map_snd_prod","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.instIsProbabilityMeasure","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_univ","MeasureTheory.Measure.withDensity","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.lintegral","MeasureTheory.lintegral_map","MeasureTheory.sigmaFinite_of_locallyFinite","MeasureTheory.withDensity_apply","MetricSpace.toEMetricSpace","Monoid.toMulAction","NNReal","NNReal.toReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.fun_comp","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","ProbabilityTheory.indepFun_iff_hasLaw_prodMk_prod","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddGroup","Real.instCompleteSpace","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Semiring.toMonoid","Set","Set.univ","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_id","congrArg","congrFun'","eq_self","id","instDistribOfSemiring","instHMul","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instProperSpaceReal","instR1Space","instSMulOfMul","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurable_pi_apply","of_eq_true","one_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltConditionalCentering","name":"GinibrePoincare.gaussianVectorPredictableTilt_centered_lintegral","type_dependencies":["AEMeasurable","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HMul.hMul","HSub.hSub","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.lintegral","NNReal","NNReal.toReal","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","Prod","Prod.instMeasurableSpace","Prod.mk","Real","Real.instMul","Real.instSub","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHSub"],"value_dependencies":["AEMeasurable","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub","ContinuousSub.measurableSub\u2082","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instMeasurableMul\u2082","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.trans","Field.toSemifield","Finset","Finset.instSetLike","Finset.measurable_prod","Finset.prod","Finset.univ","Fintype","GinibrePoincare.gaussianExponentialTilt","GinibrePoincare.gaussianExponentialTilt._proof_1","GinibrePoincare.gaussianVectorExponentialTilt","GinibrePoincare.gaussianVectorExponentialTilt_centered_lintegral","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.const_mul","Measurable.div_const","Measurable.ennreal_ofReal","Measurable.exp","Measurable.fst","Measurable.fun_comp","Measurable.fun_mul","Measurable.fun_sub","Measurable.mul_const","Measurable.of_eval","Measurable.pow_const","Measurable.prodMk","Measurable.snd","Measurable.sub_const","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.lintegral","MeasureTheory.lintegral_const_mul","MeasureTheory.lintegral_prod","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instMeasurableSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSemiring.toSemigroupWithZero","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.lintegral_comp","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.hasLaw_prod","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddGroup","Real.instCommMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Semifield.toDivisionSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SetLike.instMembership","T5Space.toT1Space","T6Space.toT0Space","T6Space.toT5Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","funext","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableDiv_of_mul_inv","measurable_const","measurable_id","measurable_id'","measurable_pi_apply","mul_assoc","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralGaussianTiltJointLaw","name":"GinibrePoincare.gaussianVectorPredictableTilt_centered_map","type_dependencies":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Fintype","GinibrePoincare.gaussianVectorExponentialTilt","HMul.hMul","HSub.hSub","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.prod","MeasureTheory.Measure.withDensity","NNReal","NNReal.toReal","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","Prod","Prod.instMeasurableSpace","Prod.mk","Real","Real.instMul","Real.instSub","Real.instZero","Real.measu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","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoid.mk","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.mk","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.IsGaussianWeakClosedForm._proof_1","GinibrePoincare.IsGaussianWeakClosedForm._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianWeakClosedFormSpace._proof_1","GinibrePoincare.gaussianWeakClosedFormSpace._proof_3","GinibrePoincare.gaussianWeakClosedFormSpace._proof_4","GinibrePoincare.gaussianWeakClosedForm_add","GinibrePoincare.gaussianWeakClosedForm_smul","GinibrePoincare.gaussianWeakClosedForm_zero","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule.mk","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedFormSpace._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedFormSpace._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedFormSpace._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianWeakClosedFormSpace._proof_2","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedFormSpace._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedForm_add","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.complexGaussianMeasure","HAdd.hAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.instAdd","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.IsGaussianWeakClosedForm._proof_1","GinibrePoincare.IsGaussianWeakClosedForm._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianDbarAdjointTestL2","HAdd.hAdd","HasCompactSupport","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.denselyNormedField","Real.instRCLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","congr","congrArg","fact_one_le_two_ennreal","id","inner_add_right","instDistribOfSemiring","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormCurl","name":"GinibrePoincare.gaussianWeakClosedForm_hermiteCurl","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","HAdd.hAdd","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.sqrt","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instT2Space","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofRealCLM","Complex.ofReal_zero","ContDiff","ContDiff.comp","ContDiff.mul","ContDiff.of_le","ContDiffBump.rIn","ContDiffBump.rOut","ContDiffBumpBase","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.symm","Eq.trans","False","Field.toSemifield","Filter.Tendsto","Filter.Tendsto.congr","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_multivariateNormalized_real","GinibrePoincare.dbarComponent","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCutoff_adjointIntegral_tendsto","GinibrePoincare.gaussianWeakClosedForm_integral_identity","GinibrePoincare.ginibreSpatialCutoff","GinibrePoincare.ginibreSpatialCutoff_compact","GinibrePoincare.ginibreSpatialCutoff_smooth","GinibrePoincare.sobolevCutoff._proof_1","GinibrePoincare.sobolevCutoffBump","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.mul_right","InnerProductSpace.toNormedSpace","Inv.inv","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","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ormedField.toNormedField","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mp","Eq.mpr","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.IsGaussianWeakClosedForm._proof_1","GinibrePoincare.IsGaussianWeakClosedForm._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","GinibrePoincare.gaussianDbarAdjointTest","GinibrePoincare.gaussianDbarAdjointTestL2","GinibrePoincare.gaussianDbarAdjointTest_memLp","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Module.toDistribMulAction","MonoidWithZeroHomClass.toZeroHomClass","NNRat","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.inner_apply","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.denselyNormedField","Real.instRCLike","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomCompTriple.comp_apply","RingHomInvPair.ids","RingHomInvPair.instStarRingEnd","RingHomInvPair.triples\u2082","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","funext","id","instCommSemiringNNRat","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","map_mul","map_sub","map_zero","of_eq_true","starRingEnd","starRingEnd_self_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.gaussianWeakClosedForm_of_integral_identity","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.integral","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Algebra.toModule","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.conjCLE","Complex.conj_natCast","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.comp","ContinuousLinearEquiv","ContinuousLinearEquiv.contDiff","ContinuousLinearEquiv.equivLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm._proof_1","GinibrePoincare.IsGaussianWeakClosedForm._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","GinibrePoincare.gaussianDbarAdjointTest","GinibrePoincare.gaussianDbarAdjointTestL2","GinibrePoincare.gaussianDbarAdjointTest_memLp","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Module.toDistribMulAction","MonoidWithZeroHomClass.toZeroHomClass","NNRat","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.inner_apply","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.denselyNormedField","Real.instRCLike","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","RingHomClass.toMonoidWithZeroHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomInvPair.ids","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","congr","cong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","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianInverseSquareRootSecondSynthesisCLM","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHDiv","instHMul","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianInverseSquareRootSecondSynthesis_total_energy","GinibrePoincare.gaussianWeakDbar_hermiteCoefficient","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarWeakEquality","name":"GinibrePoincare.gaussianWeakDbar_energy_series","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","HDiv.hDiv","HMul.hMul","HPow.hPow","HasSum","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","instHDiv","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianWeakDbar_hermiteCoefficient","GinibrePoincare.hasSum_weighted_gaussianHermiteMode_of_coefficient_raise","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarWeakDomain","name":"GinibrePoincare.gaussianWeakDbar_exists_iff_summable","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","HAdd.hAdd","HMul.hMul","HPow.hPow","Iff","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instNatCast","Real.pseudoMetricSpace","Real.sqrt","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Summable","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instHPow","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","Complex.norm_mul","Complex.norm_real","Complex.ofReal","Complex.ofReal_mul","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.toReal","ENNReal.toReal_ofNat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakDbar","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteHilbertBasis","GinibrePoincare.gaussianWeakDbar_hermiteCoefficient","GinibrePoincare.gaussianWeakDbar_of_hermiteCoefficient","GinibrePoincare.hasSum_norm_sq_gaussianHermiteCoefficient","HAdd.hAdd","HMul.hMul","HPow.hPow","HasSum","HasSum.summable","HilbertBasis.repr","Iff.intro","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.apply_symm_apply","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_add","Nat.cast_mul","Nat.cast_nonneg._simp_1","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormed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inormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","T6Space.toPerfectlyNormalSpace","Top.top","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.pi_countable","TopologicalSpace.PseudoMetrizableSpace.regularSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","TopologicalSpace.metrizableSpace_pi","TopologicalSpace.pseudoMetrizableSpace_pi","True","True.intro","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","congrArg","eq_false","eq_true","fact_one_le_two_ennreal","instCountableFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instR1Space","instR1SpaceForall","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","not_false","not_false_eq_true","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarWeakEquality","name":"GinibrePoincare.gaussian_entire_compactSupport_eq_zero","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instZero","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","HasCompactSupport","LT.lt","Nat","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNontrivial","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instZero","Complex.mk","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.eq_const_of_tendsto_cocompact","Field.toSemifield","Fin","Fin.fintype","Fin.mk","Function.nontrivial","GinibrePoincare.Configuration","HasCompactSupport","HasCompactSupport.is_zero_at_infty","InnerProductSpace.toNormedSpace","LT.lt","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","Nonempty.intro","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instZero","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireRegularity","name":"GinibrePoincare.gaussian_entire_contDiff_complex_one","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","ContDiff","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENat","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","And","And.intro","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","ContDiff","Continuous","ContinuousLinearMap","ContinuousLi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dencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNormedField","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Field.toSemifield","Fin","GinibrePoincare.Configuration","Nat","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","CompactSpace","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Continuous","Continuous.add","Continuous.comp","Continuous.smul","Continuous.tendstoUniformly","ContinuousAt","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.add","Differentiable.comp","Differentiable.continuous","Differentiable.differentiableOn","Differentiable.smul_const","DifferentiableAt.hasFDerivAt","DifferentiableOn","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Eventually.of_forall","Filter.Tendsto","Fin","Fin.fintype","Finite.of_fintype","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","HAdd.hAdd","HSMul.hSMul","HasDerivAt","HasDerivAt.congr_simp","HasDerivAt.const_add","HasDerivAt.deriv","HasDerivAt.smul_const","HasFDerivAt","HasFDerivAt.comp_hasDerivAt","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsCompact","IsModuleTopology.toContinuousSMul","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addZeroClass","Pi.continuousAdd'","Pi.instAdd","Pi.instIsBoundedSMul","Pi.instZero","Pi.isScalarTower","Pi.mulAction","Pi.normedAddCommGroup","Pi.normedSpace","Pi.smulWithZero","Pi.topologicalSpace","Pi.uniformSpace","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set"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oMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set","Set.instMembership","Set.subset_univ","Set.uIcc","Set.univ","SubNegMonoid.toAddMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","add_zero","circleIntegral","circleIntegral.eq_1","circleMap","congr","congrArg","congrFun'","continuous_circleMap","continuous_const","continuous_fst","continuous_snd","deriv","deriv_circleMap","differentiable_const","differentiable_id","fderiv","funext","hasDerivAt_const_add_iff._simp_1","hasDerivAt_id","hasFDerivAt_id","id","instAddMonoidWithOneENat","instCharZeroENat","instContinuousSMulForall","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPolynormableSpace","instSMulOfMul","instTopologicalSpaceProd","instZeroENat","intervalIntegral","intervalIntegral.integral_congr","isOpen_univ","one_smul","rfl","sub_zero","zero_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireHyperplaneDivision","name":"GinibrePoincare.gaussian_entire_hyperplane_division","type_dependencies":["And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Exists","Field.toSemifield","Fin","GinibrePoincare.Configuration","HMul.hMul","Nat","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Algebra.to_smulCommClass","And","And.intro","Bool","Bool.false","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.continuous_ofReal","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff.continuous_fderiv","Continuous","Continuous.add","Continuous.clm_apply","Continuous.clm_comp","Continuous.comp","Continuous.intervalIntegrable","Continuous.mul","Continuous.smul","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.comp","ContinuousLinearMap.continuousSMul","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.id","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.mulAction","ContinuousLinearMap.restrictScalars","ContinuousLinearMap.ring","ContinuousLinearMap.smulRight","ContinuousLinearMap.sub","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.continuous","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.HasUncurry.uncurry","Function.comp","Function.hasSMul","Function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","Eq.mp","Eq.symm","Eq.trans","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.C1_pair_mem_sobolev_completion","GinibrePoincare.gaussianH1Completion_lsi_of_C2","GinibrePoincare.integral_square_eq_L2_norm_sq","GinibrePoincare.squareEntropy","GinibrePoincare.squareEntropy_congr_ae","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Integrable.congr","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Monoid.toNPow","NNReal","NNReal.instOne","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.log","Real.log_pow","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","congr","congrArg","congrFun'","deriv","eq_self","id","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat","instOneENat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BernoulliTaylorEnergy","name":"GinibrePoincare.gaussian_lsi_of_binomial_fiber_bounds","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.bernoulliTaylorEnergy","GinibrePoincare.normalizedBernoulliSum","GinibrePoincare.rademacherProduct","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","deriv","instAddNat","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["CommSemiring.toSemiring","ContDiff","ContDiff.continuous","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","Filter.Tendsto.comp","Filter.atTop","Filter.atTop_neBot","Filter.tendsto_add_atTop_nat","Function.comp","GinibrePoincare.bernoulliTaylorEnergy","GinibrePoincare.bernoulliTaylorEnergy_tendsto","GinibrePoincare.normalizedBernoulliSum","GinibrePoincare.normalizedBernoulliSum_entropy_tendsto","GinibrePoincare.rademacherProduct","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUnifor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CorrectedBrownian","GinibrePoincare.ginibreInteractionCorrectedBrownian_noise_continuous","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_contDiffAt","GinibrePoincare.ginibreOUPath_correctedBrownian_original_volterra","GinibrePoincare.ginibreQuadraticGradientPathWeight","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IntervalIntegrable","IsCompact","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","Measurable.mono","MeasurableSpace","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.AbsolutelyContinuous.ae_le","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.MemLp.of_bound","MeasureTheory.StronglyAdapted","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.ae_all_iff","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.withDensity_absolutelyContinuous","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Neg.neg","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.borelSpace","Pi.instAdd","Pi.instZero","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal._auto_1","ProbabilityTheory.IsBrownianReal.cont","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.coe_toNNReal","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.locallyFinite_volume","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_coe","Real.toNNReal_le_iff_le_coe","Real.toNNReal_zero","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toMonoid","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","Subtype.property","Subtype.val","Top.top","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithTop.some","Zero.toOfNat0","abs","abs_le_of_sq_le_sq","autoParam","congr","congrArg","congrFun'","continuous_iff_continuousAt","continuous_real_toNNReal","id","instAddNat","instCommCStarAlgebraComplex","instCountableFin","instCountableProd"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UnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HSMul.hSMul","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarRing.to_normedStarGroup","CommMagma.toMul","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.conj_ofReal","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.coeFn_star","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminorm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inibre_distributional_gradient_exists_supported_representative","GinibrePoincare.ginibre_distributional_gradient_mul","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasCompactSupport","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","IsClosed.mem_of_tendsto","IsTopologicalAddGroup.toContinuousAdd","LE.le","LE.le.trans","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.AEStronglyMeasurable.congr","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.aestronglyMeasurable","MeasureTheory.Lp.coeFn_add","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommGroup","Pi.instAdd","Pi.topologicalSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instSMul","Zero.toOfNat0","add_zero","closure","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","funext","id","instArchimedeanNat","instFintypeProd","instHAdd","instHMul","instHSMul","instInhabitedNat","instIsDirectedOrder","instLTNat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceProd","isClosed_closure","nhds","of_eq_true","rfl","subset_closure","tsupport","tsupport_mul_subset_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticContinuousFieldIntegral","name":"GinibrePoincare.ginibreBoundedField_continuous_integral_exists","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Continuous","ContinuousENorm.toENorm","ContinuousOn","DecidableEq","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Filter.Eventually","Filter.EventuallyEq","Filter.atTop","Finset.sum","Finset.univ","Fintype","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","HAdd.hAdd","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instLE","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.no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oLattice","DFunLike.coe","ENNReal","ENNReal.instZero","Eq","GinibrePoincare.ginibreBrownianFamilyPastSpace","GinibrePoincare.ginibreBrownianFamilyPastSpace_mono","LE.le","Lattice.toSemilatticeSup","MeasurableSpace","MeasurableSpace.generateFrom","MeasurableSpace.instCompleteLattice","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","NNReal","NNReal.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Set","Set.ofPred","Zero.toOfNat0","sup_le_sup_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticPastAugmentation","name":"GinibrePoincare.ginibreBrownianAugmentedFiltration._proof_2","type_dependencies":["GinibrePoincare.ginibreBrownianFamilyPastSpace","GinibrePoincare.ginibreNullAugmentation","LE.le","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","ProbabilityTheory.IsPreBrownianReal","Real"],"value_dependencies":["GinibrePoincare.ginibreBrownianFamilyPastSpace","GinibrePoincare.ginibreBrownianFamilyPastSpace_le","GinibrePoincare.ginibreNullAugmentation_le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","ProbabilityTheory.IsPreBrownianReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralConditional","name":"GinibrePoincare.ginibreBrownianAugmentedFiltration.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.ginibreBrownianAugmentedFiltration","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","Real"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.ginibreBrownianAugmentedFiltration","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedVariation","name":"GinibrePoincare.ginibreBrownianAugmentedMixedError","type_dependencies":["Fin","HAdd.hAdd","NNReal","Nat","OfNat.ofNat","Real","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedHessian","name":"GinibrePoincare.ginibreBrownianAugmentedMixedError.eq_1","type_dependencies":["Eq","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreBrownianAugmentedMixedError","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HMul.hMul","HSub.hSub","NNReal","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHSub","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.ginibreBrownianAugmentedMixedError","HAdd.hAdd","NNReal","Nat","OfNat.ofNat","Real","instAddNat","instHAdd","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedVariation","name":"GinibrePoincare.ginibreBrownianAugmentedMixedError_memLp_two","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.val","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedMixedError","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MemLp","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.measurableSpace","Real.norm","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing"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ithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Decidable.decide","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype","Fintype.card_fin","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedMixedError","GinibrePoincare.ginibreBrownianUniformTime_increment_coe","GinibrePoincare.ginibreBrownian_augmented_mixed_sum_secondMoment_le","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_mono","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","LE","LE.le","LT.lt","List.nil","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_ofNat","Mathlib.Tactic.FieldSimp.zpow'_one","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.addLeftMono","NNReal.instCommSemiring","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NNReal.toReal","NPow.toPow","NSMul.toSMul","Nat","Nat.ble","Nat.cast","Nat.cast_add","Nat.cast_nonneg'","Nat.cast_one","Nat.le_succ","Nat.succ_le_of_lt","Ne","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocSemiring.toDistrib","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.mk","Prod.snd","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.partialOrder","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","True","Zero.toOfNat0","add_tsub_cancel_of_le","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","div_one","eq_of_heq","eq_self","funext","id","inferInstance","instAddNat","instDecidableEqNat","instDecidableNot","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsCancelMulZero","instLTFin","instOfNat","instOfNatNat","instStarRingNNReal","mul_one","ne_of_gt","nsmul_eq_mul","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedVariation","name":"GinibrePoincare.ginibreBrownianAugmentedMixedError_tendstoInProbability","type_dependencies":["EMetricSpace.toPseudoEMetric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ugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedQuadraticError","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Decidable.decide","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedQuadraticError","GinibrePoincare.ginibreBrownianUniformTime_increment_coe","GinibrePoincare.ginibreBrownian_augmented_quadratic_sum_secondMoment_le","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_mono","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","LE","LE.le","LT.lt","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_ofNat","Mathlib.Tactic.FieldSimp.zpow'_one","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.addLeftMono","NNReal.instCommSemiring","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NNReal.toReal","NPow.toPow","NSMul.toSMul","Nat","Nat.ble","Nat.cast","Nat.cast_add","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.le_succ","Nat.succ_le_of_lt","Ne","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocSemiring.toDistrib","Norm.norm","NormedAddComm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anSquare","type_dependencies":["Filter.Tendsto","Filter.atTop","Fin","Fin.val","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedQuadraticError","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NPow.toPow","Nat","Nat.instPreorder","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Algebra.id","Algebra.toModule","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Distrib.toAdd","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","Eq.mp","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Fin","Fin.val","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedQuadraticError","GinibrePoincare.ginibreBrownianAugmentedQuadraticError_secondMoment_le","GinibrePoincare.ginibreUniformBrownianTime","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.nnrat","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","MeasureTheory.integral_nonneg","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","instAddNat","instClosedIciTopology","instCommSemiringNNRat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHasSolidNormReal","instIsOrderedModule","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","mul_one_div","nhds","normedAlgebraRat","sq_nonneg","squeeze_zero","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedDiagonal","name":"GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal","type_dependencies":["NNReal","Nat","Real"],"value_dependencies":["Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedHessian","name":"GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal.eq_1","type_dependencies":["Eq","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal","NNReal","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedDiagonal","name":"GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal_tendstoInProbability","type_dependencies":["Continuous","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.Eventually","Filter.atTop","Fintype","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.StronglyAdapted","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.instPreorder","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.toNNReal","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Continuous","Continuous.comp","Continuous.continuousOn","ContinuousENorm.toENorm","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter","Filter.Eventually","Filter.Eventually.of_forall","Filter.Tendsto","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.val","Finset","Finset.aestronglyMeasurable_sum","Finset.instSetLike","Finset.sum","Finset.sum_add_distrib","Finset.sum_apply","Finset.sum_congr","Finset.univ","Fintype","Function.comp","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianAugmentedQuadraticError","GinibrePoincare.ginibreBrownianAugmentedQuadraticError_memLp_two","GinibrePoincare.ginibreBrownianAugmentedQuadraticError_tendstoInProbability","GinibrePoincare.ginibreBrownianAugmentedWeightedDiagonal","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoContinuousScalarRiemann_fin_tendsto","GinibrePoincare.itoTendstoInMeasure_add","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","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e.eq_1","type_dependencies":["Eq","GinibrePoincare.ginibreBrownianFamilyPastSpace","MeasurableSpace","MeasurableSpace.comap","MeasurableSpace.pi","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Prod","Prod.fst","Prod.snd","Real","Real.measurableSpace","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","inferInstance"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreBrownianFamilyPastSpace","MeasurableSpace","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyFiltration","name":"GinibrePoincare.ginibreBrownianFamilyPastSpace_le","type_dependencies":["GinibrePoincare.ginibreBrownianFamilyPastSpace","LE.le","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","ProbabilityTheory.IsPreBrownianReal","Real","inferInstance"],"value_dependencies":["AEMeasurable","Iff.mp","Measurable","Measurable.comap_le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.aemeasurable","Prod","Prod.fst","Prod.snd","Real","Real.measurableSpace","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","aemeasurable_iff_measurable","inferInstance","measurable_pi_lambda"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyFiltration","name":"GinibrePoincare.ginibreBrownianFamilyPastSpace_mono","type_dependencies":["GinibrePoincare.ginibreBrownianFamilyPastSpace","MeasurableSpace","MeasurableSpace.instPartialOrder","Monotone","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Real"],"value_dependencies":["Eq","Eq.mpr","Eq.symm","Function.comp","GinibrePoincare.ginibreBrownianFamilyPastSpace","LE.le","LE.le.trans","Measurable","Measurable.comap_le","Measurable.of_eval","MeasurableSpace","MeasurableSpace.comap","MeasurableSpace.comap_comp","MeasurableSpace.comap_mono","MeasurableSpace.instLE","MeasurableSpace.instPartialOrder","MeasurableSpace.pi","Membership.mem","NNReal","NNReal.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","Real","Real.instLE","Real.instZero","Real.measurableSpace","Real.partialOrder","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.mk","Subtype.property","Subtype.val","Zero.toOfNat0","congrArg","id","inferInstance","measurable_pi_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticFamilyQuadraticSum","name":"GinibrePoincare.ginibreBrownianFamilyQuadraticSum","type_dependencies":["Fintype","NNReal","Nat","Real"],"value_dependencies":["Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instSub","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticFamilyQuadraticSum","name":"GinibrePoincare.ginibreBrownianFamilyQuadraticSum.eq_1","type_dependencies":["Eq","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instSub","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat"],"value_dependencies":["Eq.refl","Fintype","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","NNReal","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticFamilyQuadraticSum","name":"GinibrePoincare.ginibreBrownianFamilyQuadraticSum_tendstoInProbability","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","Fintype","Fintype.card","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","HMul.hMul","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoEMetricSpace.toUniformSpace","Real","Real.instMul","Real.instNatCast","Real.measurableSpace","Real.metricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass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inibreBrownianHamiltonian_continuous_ito_martingale_exists","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Continuous","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Filter.Eventually","Filter.EventuallyEq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreRealPaperSpeedGenerator","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.ae","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instLE","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.toNNReal","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And","And.casesOn","And.intro","And.left","And.right","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","ContDiffAt.contDiffWithinAt","ContDiffAt.of_le","ContDiffOn","Continuous","ContinuousENorm.toENorm","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Filter.Eventually","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GT.gt","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianFullContinuousNoise_ae","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop_survival_measurable","GinibrePoincare.ginibreBrownianHamiltonianStoppedDrift_bounded","GinibrePoincare.ginibreBrownianHamiltonianStoppedDrift_continuous","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_continuous","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_equation_ae","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_initial","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_range","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_stronglyAdapted","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreCompactVolterra_continuous_ito_martingale_exists","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationTestCompensator","GinibrePoincare.ginibreConfigurationTestCompensator_eq_generator","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_le","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianSublevel","GinibrePoincare.ginibreHamiltonianSublevel_isCompact","GinibrePoincare.ginibreHamiltonian_contDiffAt","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.isOpen_collisionFree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Interva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Instance","instArchimedeanNat","instClosedIciTopology","instCommSemiringNNRat","instCountableNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instHasSolidNormReal","instInhabitedNat","instIsDirectedOrder","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","le_antisymm","le_of_lt","le_of_not_gt","lt_of_le_of_lt","lt_of_not_ge","mul_nonneg","mul_one_div","neg_neg_of_pos","nhds","normedAlgebraRat","rfl","tendsto_const_nhds","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianStoppingExitMaximalAdaptation","name":"GinibrePoincare.ginibreBrownianMaximalProcess","type_dependencies":["Fin","GinibrePoincare.Configuration","NNReal","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreDrivenMaximalValue","NNReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianPrefix","name":"GinibrePoincare.ginibreBrownianMaximalProcess.eq_1","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreDrivenMaximalValue","NNReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","NNReal","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCIRRealization","name":"GinibrePoincare.ginibreBrownianMaximalProcess_CIR_realization","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Continuous","ContinuousENorm.toENorm","Distrib.toAdd","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Filter.Eventually","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.integral","MetricSpace.toEMetricSpace","Monoid.toNPow","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDi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ibrePoincare.Configuration","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreCenterSquareRootRegularized","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreSquareRootCenter","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instLE","Real.instLT","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.toNNReal","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instHAdd","instHSub","instLENat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","And.left","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiff.contDiffOn","ContDiff.of_le","ContDiffOn","Continuous","Continuous.intervalIntegrable","ContinuousENorm.toENorm","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Filter.Eventually","Filter.EventuallyEq","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.contDiff_ginibreCenterSquareRootRegularized","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_continuous","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_range","GinibrePoincare.ginibreBrownianMaximalProcess_local_test_ito_integral_exists","GinibrePoincare.ginibreCenterRegularizedIto_positive_start_increment","GinibrePoincare.ginibreCenterRegularized_generator_continuous","GinibrePoincare.ginibreCenterSquareRootRegularized","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.ginibreSquareRootCenter","HAdd.hAdd","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","LE.le","LE.le.trans","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Preorder.toLE","ProbabilityTheory.IsBrownianRe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ianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.toNNReal","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"],"value_dependencies":["And","And.intro","And.left","And.right","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Continuous","Continuous.continuousOn","Eq","Eq.mp","Eq.mpr","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownianMaximalProcess_global_original_solution","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreDrivenPath_finite_interval_unique","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","InnerProductSpace.toNormedSpace","IntervalIntegrable","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.StronglyAdapted","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toENormedAddMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_zero","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instCommCStarAlgebraComplex","instHAdd","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","intervalIntegral","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCIRDrivenLocal","name":"GinibrePoincare.ginibreBrownianMaximalProcess_local_CIR_Brownian_integral","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Continuous","ContinuousENorm.toENorm","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.Eventually","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreRecenteredRadialDirection","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.integral","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp.innerProductSpace._proof_1","PiLp.instNorm","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Pseudo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ianTime","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NNReal.instSemiring","NNReal.instSub","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.semiring","Semiring.toAddCommMonoid","Semiring.toMonoid","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOURiemann","name":"GinibrePoincare.ginibreBrownianOURiemannVariance._proof_1","type_dependencies":["DistribLattice.toLattice","Fin","Fin.val","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HPow.hPow","LE.le","Lattice.toSemilatticeInf","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.linearOrder","Real.semiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Zero.toOfNat0","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHPow","instMulZeroClassOfSemiring","instOfNatNat"],"value_dependencies":["CommRing.toNonUnitalCommRing","Fin","Fin.val","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","NNReal","NNReal.toReal","Nat","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","Real","Real.commRing","Real.instAddCommMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instPreorder","Real.instStarOrderedRing","Real.linearOrder","Real.partialOrder","Real.semiring","StarOrderedRing.toExistsAddOfLE","instAddNat","instHAdd","instOfNatNat","instStarRingReal","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOURiemann","name":"GinibrePoincare.ginibreBrownianOURiemannVariance_coe","type_dependencies":["Eq","Finset.range","Finset.sum","GinibrePoincare.ginibreBrownianOURiemannVariance","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"],"value_dependencies":["Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.trans","Fin","Fin.fintype","Fin.sum_univ_eq_sum_range","Fin.val","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.ginibreBrownianOURiemannVariance","GinibrePoincare.ginibreBrownianOURiemannVariance._proof_1","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_coe","GinibrePoincare.ginibreUniformBrownianTime_mono","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Membership.mem","Monoid.toNPow","NNReal","NNReal.coe_sub","NNReal.coe_sum","NNReal.instSemiring","NNReal.instSub","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","Nat.le_succ","Nat.succ","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instSub","Real.semiring","Semiring.toAddCommMonoid","Semiring.toMonoid","SetLike.instMembership","congr","congrArg","congrFun'","id","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOURiemann","name":"GinibrePoincare.ginibreBrownianOURiemannVariance_tendsto","type_dependencies":["Filter.Tendsto","Filter.atTop","GinibrePoincare.ginibreBrownianOURiemannVariance","GinibrePoincare.ginibreOUVariance","NNReal","NNReal.instTopologicalSpace","Nat","Nat.instPreorder","nhds"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous","Continuous.comp'","Continuous.const_mul","Continuous.fun_pow","Continuous.fun_sub","Continuous.rexp","Continuous.tendsto","Eq.mp","Eq.trans","Filter","Filter.Tendsto","Filter.Tendsto.comp","Filter.atTop","Finset.range","Finset.sum","Function.comp","GinibrePoincare.ginibreBrownianOURiemannVariance","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreOUStochasticWeight_sq_hasDerivAt","GinibrePoincare.ginibreOUStochasticWeight_variance_integral","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreUniformScalarRiemann_tendsto","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NNReal.coe_nonneg","NNReal.instTopologicalSpace","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.sqrt","Real.toNNReal","Real.toNNReal_coe","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreStochasticOURiemann.0.GinibrePoincare.ginibreBrownianOURiemannVariance_tendsto._simp_1_1","congr","congrArg","congrFun'","continuous_const","continuous_id'","continuous_real_toNNReal","funext","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOURiemann","name":"GinibrePoincare.ginibreBrownianOURiemann_isGaussianProcess","type_dependencies":["GinibrePoincare.ginibreBrownianOURiemannSum","MeasurableSpace","MeasureTheory.Measure","NNReal","Nat","ProbabilityTheory.IsGaussianProcess","ProbabilityTheory.IsPreBrownianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Semiring.toModule","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","And","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.sub","DFunLike.coe","Eq","Eq.refl","Eq.trans","Exists","Exists.intro","Fin","Fin.fintype","Fin.val","Finset","Finset.image","Finset.instSetLike","Finset.instUnion","Finset.mem_image","Finset.mem_union_left","Finset.mem_union_right","Finset.mem_univ","Finset.restrict","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.ginibreBrownianOURiemannSum","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LinearOrder.toDecidableEq","MeasurableSpace","MeasureTheory.Measure","Membership.mem","MulZeroClass.toMul","NNReal","NNReal.instLinearOrder","NNReal.toReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNonAssocSemiring.toMulZeroClass","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","ProbabilityTheory.IsGaussianProcess.of_isGaussianProcess","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.instRing","Real.instSub","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","True","UniformSpace.toTopologicalSpace","Union.union","congrArg","eq_self","instAddNat","instHAdd","instHMul","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","of_eq_true","rfl","smul_apply","sub_apply","sum_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOURiemann","name":"GinibrePoincare.ginibreBrownianOURiemann_second_moment","type_dependencies":["Eq","GinibrePoincare.ginibreBrownianOURiemannSum","GinibrePoincare.ginibreBrownianOURiemannVariance","HPow.hPow","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","Monoid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.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","CommRing.toNonUnitalCommRing","Continuous","Continuous.comp","Continuous.mul","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Filter","Filter.Tendsto","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","GinibrePoincare.drivenOUCorrection","GinibrePoincare.drivenOUCorrection_zero","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath_compensated_square_leftSums","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.cont","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.eval_zero_ae_eq_zero","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_zero","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","continuous_const","continuous_real_toNNReal","funext","id","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","nhds","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUProcess","name":"GinibrePoincare.ginibreBrownianOU_gaussian_initial_isGaussianProcess","type_dependencies":["GinibrePoincare.ginibreBrownianOU","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","NNReal","NNReal.toReal","ProbabilityTheory.HasGaussianLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsGaussianProcess","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Semiring.toModule","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.trans","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath_initial_split","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_zero_isGaussianProcess","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUConvolutionFunctional_ae_eq","GinibrePoincare.ginibreOUConvolutionFunctional_measurable","GinibrePoincare.ginibreOUDecay","GinibrePoincare.independent_gaussian_initial_process_isGaussianProcess","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Measurable","Measurable.of_eval","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.toReal","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","ProbabilityTheory.HasGaussianLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsGaussianProcess","ProbabilityTheory.IsGaussianProcess.congr","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instAdd","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","SMulZeroClass.toSMul","Semiring.toModule","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHAdd","instHMul","instHSMul","measurable_id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUConvolution","name":"GinibrePoincare.ginibreBrownianOU_hasLaw","type_dependencies":["DFunLike.coe","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUTransition","MeasurableSpace","MeasureTheory.Measure","NNReal","NNReal.toReal","ProbabilityTheory.HasLaw","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","Real","Real.measurableSpace","Real.sqrt"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Filter.univ_mem'","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_zero_hasLaw","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.HasLaw.congr","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_add_const","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.exp","Real.instAdd","Real.instAddMonoid","Real.instCommSemiring","Real.instMul","Real.instNeg","Real.instRCLike","Real.instRing","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.semiring","Real.sqrt","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","autoParam","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","intervalIntegral","rfl","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUIndependent","name":"GinibrePoincare.ginibreBrownianOU_independent","type_dependencies":["GinibrePoincare.ginibreBrownianOU","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","NNReal","NNReal.toReal","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Real","Real.measurableSpace","Real.sqrt"],"value_dependencies":["Function.comp","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUValueFunctional","GinibrePoincare.ginibreOUValueFunctional_ae_eq","GinibrePoincare.ginibreOUValueFunctional_measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","NNReal","NNReal.toReal","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.congr","ProbabilityTheory.IsBrownianReal","Real","Real.measurableSpace","Real.sqrt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPlanarInnovation","name":"GinibrePoincare.ginibreBrownianOU_innovation_past_block","type_dependencies":["And","Exists","Filter.EventuallyEq","GinibrePoincare.ginibreBrownianOUInnovation","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","ProbabilityTheory.IsBrownianReal","Prod","Prod.instMeasurableSpace","Prod.mk","Real","Real.measurableSpace","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val"],"value_dependencies":["And","And.intro","ContinuousSub.measurableSub\u2082","Distrib.toAdd","Eq","Exists.intro","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUConvolutionFunctional_ae_eq","GinibrePoincare.ginibreOUConvolutionFunctional_measurable","HAdd.hAdd","HSub.hSub","IsTopologicalAddGroup.to_continuousSub","Measurable","Measurable.comp","Measurable.fun_sub","Measurable.of_eval","Measurable.prodMk","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.shift","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddGroup","Real.instSub","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.sqrt","Set","Set.Elem","Set.Iic","Set.instMembership","Set.ofPred","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHSub","instIsTopologicalAddGroupReal","instSecondCountableTopologyReal","measurable_pi_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUQuadraticConditional","name":"GinibrePoincare.ginibreBrownianOU_memLp_two","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.ginibreBrownianOU","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.MemLp","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","ContinuousENorm.toENorm","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.mp","Eq.symm","Function.comp","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_hasLaw","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.memLp_map_measure_iff","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsGaussian.memLp_two_id","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instCompleteSpace","Real.instMul","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","aestronglyMeasurable_id","congrArg","id","instHMul","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPlanarInnovation","name":"GinibrePoincare.ginibreBrownianOU_planar_innovations_hasLaw","type_dependencies":["GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreOUVariance","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.prod","NNReal","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","Prod","Prod.instMeasurableSpace","Prod.mk","Real","Real.instZero","Real.measurableSpace","Zero.toOfNat0"],"value_dependencies":["And","And.casesOn","Exists","Exists.casesOn","Filter.EventuallyEq","Function.comp","GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreBrownianOUInnovation_hasLaw","GinibrePoincare.ginibreBrownianOU_innovation_past_block","GinibrePoincare.ginibreOUVariance","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Membership.mem","NNReal","NNReal.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.congr","ProbabilityTheory.IndepFun.hasLaw_prod","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Semiring.toModule","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","measurable_fst"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPlanarInnovation","name":"GinibrePoincare.ginibreBrownianOU_planar_innovations_independent_past","type_dependencies":["GinibrePoincare.ginibreBrownianOUInnovation","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Prod","Prod.instMeasurableSpace","Prod.mk","Real","Real.measurableSpace","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val"],"value_dependencies":["AEMeasurable","And","And.casesOn","Exists","Exists.casesOn","Filter.EventuallyEq","Function.comp","GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreBrownianOUInnovation_hasLaw","GinibrePoincare.ginibreBrownianOUInnov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easureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_prod_map","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsProbabilityMeasure","MeasureTheory.StronglyMeasurable.aestronglyMeasurable","MeasureTheory.ae","MeasureTheory.ae_of_ae_map","MeasureTheory.condExp","MeasureTheory.condExp_congr_ae","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_map","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.toReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_map_const_add","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.map","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instInhabited","Real.instLE","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Elem","Set.Iic","Set.instMembership","Set.ofPred","StandardBorelSpace.prod","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_iff_measurable","congrArg","id","instHAdd","instHMul","instIsTopologicalRingReal","instNonemptyOfInhabited","instNonemptyProd","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurable_const","measurable_fst","measurable_id'","measurable_pi_lambda","measurable_snd","standardBorel_of_polish","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPlanarMarkov","name":"GinibrePoincare.ginibreBrownianOU_planar_whole_past_markov_integrable","type_dependencies":["DFunLike.coe","Filter.EventuallyEq","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibrePlanarBrownianPastMeasurableSpace","HAdd.hAdd","InnerProductSpace.toNormedSpace","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.integral","NNReal","NNReal.toReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instHAdd"],"value_dependencies":["AEMeasurable","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","ContinuousAdd.measurableAdd","ContinuousAdd.measurableMul\u2082","ContinuousMul.measurableMul\u2082","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Filter.Eventually","Filter.EventuallyEq","Filter.EventuallyEq.trans","Filter.mp_mem","Filter.univ_mem'","Function.comp","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreBrownianOU_planar_innovations_hasLaw","GinibrePoincare.ginibreBrownianOU_planar_innovations_independent_past","GinibrePoincare.ginibreBrownianOU_step_ae","GinibrePoincare.ginibreIndependent_condDistrib_general","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUPastFunctional","GinibrePoincare.ginibreOUPastFunctional_ae_eq","GinibrePoincare.ginibreOUPastFunctional_measurable","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibrePlanarBrownianPastMeasurableSpace","HAdd.hAdd","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.add","Measurable.aemeasurable","Measurable.comp","Measurable.const_add","Measurable.mul","Measurable.prodMap","Measurable.prodMk","Measurable.stronglyMeasurable","MeasurableSpace","MeasurableSpace.comap","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.congr","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_prod_map","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsProbabilityMeasure","MeasureTheory.StronglyMeasurable.aestronglyMeasurable","MeasureTheory.ae","MeasureTheory.ae_of_ae_map","MeasureTheory.condExp","MeasureTheory.condExp_congr_ae","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integral","MeasureTheory.integral_map","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.toReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_map_const_add","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.map","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instInhabited","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Elem","Set.Iic","Set.instMembership","Set.ofPred","StandardBorelSpace.prod","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_iff_measurable","congrArg","id","instHAdd","instHMul","instIsTopologicalRingReal","instNonemptyOfInhabited","instNonemptyProd","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurable_const","measurable_fst","measurable_id'","measurable_pi_lambda","measurable_snd","standardBorel_of_polish","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUQuadraticVariation","name":"GinibrePoincare.ginibreBrownianOU_quadratic_variation_noise","type_dependencies":["Filter.Eventually","Filter.Tendsto","Filter.atTop","Finset.range","Finset.sum","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instPreorder","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instSub","Real.instZero","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat","nhds"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous","Continuous.comp","Continuous.mul","Filter.Tendsto","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Finset.range","Finset.sum","GinibrePoincare.drivenOUPath_quadratic_variation_noise","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HPow.hPow","HSub.hSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NNReal","NNReal.instTopologicalSpace","NPow.toPow","Nat","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.cont","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instSub","Real.instZero","Real.pseudoMetricSpace","Real.toNNReal","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_const","continuous_real_toNNReal","id","instAddNat","instHAdd","instHPow","instHSub","instIsTopologicalRingReal","instOfNatNat","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUFunctional","name":"GinibrePoincare.ginibreBrownianOU_shift_independent_past","type_dependencies":["Distrib.toAdd","GinibrePoincare.ginibreBrownianOU","HAdd.hAdd","HSub.hSub","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Real","Real.instSub","Real.instZero","Real.measurableSpace","Real.sqrt","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHSub"],"value_dependencies":["Distrib.toAdd","Eq","Filter.Eventually.of_forall","Function.comp","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUConvolutionFunctional_ae_eq","GinibrePoincare.ginibreOUConvolutionFunctional_measurable","HAdd.hAdd","HSub.hSub","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.congr","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.shift","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.indepFun_shift","Real","Real.instSub","Real.instZero","Real.measurableSpace","Real.sqrt","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","Zero.toOfNat0","id","instDistribOfSemiring","instHAdd","instHSub","measurable_id","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUContinuousReversal","name":"GinibrePoincare.ginibreBrownianOU_stationary_continuous_horizon_law_reversal","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousMap","ContinuousMap.comp","Eq","GinibrePoincare.ginibreBrownianOUHorizonPath","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.instMeasurableSpaceContinuousMapElemNNRealIccOfNatReal_ginibrePoincare","HDiv.hDiv","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","Membership.mem","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHDiv","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CompactSpace.sigmaCompact","CompactlyCoherentSpace.of_sequentialSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","Continuous.measurable","ContinuousEvalConst.continuous_eval_const","ContinuousMap","ContinuousMap.comp","ContinuousMap.compactConvergenceUniformSpace","ContinuousMap.compactOpen","ContinuousMap.instCompleteSpaceOfCompactlyCoherentSpace","ContinuousMap.instContinuousEvalConst","ContinuousMap.instFunLike","ContinuousMap.instIsCountablyGeneratedProdUniformityOfWeaklyLocallyCompactSpaceOfSigmaCompactSpace","ContinuousMap.instSeparableSpace","ContinuousMap.instT0Space","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","FirstCountableTopology.frechetUrysohnSpace","FrechetUrysohnSpace.to_sequentialSpace","GinibrePoincare.continuousMap_law_eq_of_whole_domain_path_law_eq","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOUHorizonPath","GinibrePoincare.ginibreBrownianOUHorizonPath_ae","GinibrePoincare.ginibreBrownianOUHorizonPath_measurable","GinibrePoincare.ginibreBrownianOU_stationary_whole_horizon_law_reversal","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.ginibre_measurable_continuousMap_of_evaluations","GinibrePoincare.instBorelSpaceContinuousMapElemNNRealIccOfNatReal_ginibrePoincare","GinibrePoincare.instMeasurableSpaceContinuousMapElemNNRealIccOfNatReal_ginibrePoincare","GinibrePoincare.instNonemptyElemNNRealIccOfNat_ginibrePoincare","HDiv.hDiv","HSub.hSub","Measurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_congr","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instDiv","NNReal.instOne","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instSecondCountableTopology","NNReal.instSemiring","NNReal.instSub","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.hasGaussianLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","Subtype.instFrechetUrysohnSpace","Subtype.pseudoMetricSpace","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","congrArg","funext","id","instHDiv","instHSub","instMetricSpaceNNReal","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instPseudoMetricSpaceNNReal","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopologicalSpaceSubtype","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","proper_of_compact"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUCovariance","name":"GinibrePoincare.ginibreBrownianOU_stationary_covariance","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","Eq","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUDecay","HDiv.hDiv","HSub.hSub","Max.max","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","Min.min","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","NNReal.instSemiring","NNReal.instSub","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.covariance","ProbabilityTheory.gaussianReal","Real","Real.instDivInvMonoid","Real.instNatCast","Real.instZero","Real.measurableSpace","Real.sqrt","SemilatticeInf.toMin","SemilatticeSup.toMax","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHDiv","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toNonUnitalCommSemiring","Distrib.toAdd","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr","Eq.symm","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_stationary_covariance_step","GinibrePoincare.ginibreOUDecay","HAdd.hAdd","HDiv.hDiv","HSub.hSub","LE.le","LinearOrder.toPartialOrder","Max.max","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","Min.min","NNReal","NNReal.addLeftMono","NNReal.coe_add","NNReal.instCommSemiring","NNReal.instDiv","NNReal.instLinearOrder","NNReal.instOne","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.covariance","ProbabilityTheory.covariance_comm","ProbabilityTheory.gaussianReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instNatCast","Real.instZero","Real.measurableSpace","Real.sqrt","SemilatticeInf.toMin","SemilatticeSup.toMax","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","Zero.toOfNat0","add_tsub_cancel_of_le","congr","congrArg","congrFun'","id","instDistribOfSemiring","instHAdd","instHDiv","instHSub","instOfNatAtLeastTwo","instOfNatNat","instStarRingNNReal","le_total","max_eq_left","max_eq_right","min_eq_left","min_eq_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUCovariance","name":"GinibrePoincare.ginibreBrownianOU_stationary_covariance_step","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","Eq","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUDecay","HAdd.hAdd","HDiv.hDiv","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemiring","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.covariance","ProbabilityTheory.gaussianReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instNatCast","Real.instZero","Real.measurableSpace","Real.sqrt","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHAdd","instHDiv","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.hasSMul","GinibrePoincare.drivenOUPath","GinibrePoincare.drivenOUPath_initial_split","GinibrePoincare.ginibreBrownianNoise","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOU_zero_covariance_step","GinibrePoincare.ginibreBrownianOU_zero_independent_initial","GinibrePoincare.ginibreBrownianOU_zero_isGaussianProcess","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUDecay_add","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance_coe","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.MemLp.add","MeasureTheory.MemLp.aemeasurable","MeasureTheory.MemLp.const_smul","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulActionWithZero","MonoidWithZero.toMulZeroOneClass","MulActionWithZero.toSMulWithZero","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNRat.rawCast","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemifield","NNReal.instSemiring","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","ProbabilityTheory.HasGaussianLaw.memLp_two","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.hasGaussianLaw","ProbabilityTheory.HasLaw.variance_eq","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.covariance_eq_zero","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_eval","ProbabilityTheory.covariance","ProbabilityTheory.covariance_add_left","ProbabilityTheory.covariance_add_right","ProbabilityTheory.covariance_comm","ProbabilityTheory.covariance_self","ProbabilityTheory.covariance_smul_left","ProbabilityTheory.covariance_smul_right","ProbabilityTheory.gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","ProbabilityTheory.variance","ProbabilityTheory.variance_id_gaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Rat.rawCast","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAdd","Real.instAddCommMonoid","Real.instCommSemiring","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulWithZero.toSMulZeroClass","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","one_div","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUFiniteLaw","name":"GinibrePoincare.ginibreBrownianOU_stationary_finite_law_reversal","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fintype","GinibrePoincare.ginibreBrownianOU","HDiv.hDiv","HSub.hSub","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","Real","Real.instZero","Real.measurableSpace","Real.sqrt","Semiring.toNonAssocSemiring","WithLp","WithLp.measurableSpace","WithLp.toLp","Zero.toOfNat0","instHDiv","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoidWithOne.toNatCast","CommSemiring.toNonUnitalCommSemiring","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Fintype","GinibrePoincare.gaussianEuclidean_law_eq_of_coordinate_mean_covariance","Gi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UPastFunctional_measurable","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","HAdd.hAdd","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Measurable","Measurable.add","Measurable.aemeasurable","Measurable.comp","Measurable.comp_aemeasurable","Measurable.mul","Measurable.stronglyMeasurable","MeasurableSpace","MeasurableSpace.comap","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.mono'","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.StronglyMeasurable.aestronglyMeasurable","MeasureTheory.ae","MeasureTheory.ae_of_ae_map","MeasureTheory.condExp","MeasureTheory.condExp_congr_ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_map","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.toReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_map_const_add","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instInhabited","Real.instLE","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Elem","Set.Iic","Set.instMembership","Set.ofPred","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_id","aemeasurable_iff_measurable","congrArg","id","instHAdd","instHMul","instIsTopologicalRingReal","instNonemptyOfInhabited","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","measurable_const","measurable_fst","measurable_pi_lambda","measurable_snd","standardBorel_of_polish","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUCovariance","name":"GinibrePoincare.ginibreBrownianOU_zero_covariance_step","type_dependencies":["Eq","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","HAdd.hAdd","HMul.hMul","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","NNReal","NNReal.toReal","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.covariance","Real","Real.instAdd","Real.instMul","Real.instZero","Real.sqrt","Zero.toOfNat0","instHAdd","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","ContinuousENorm.toENorm","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Function.hasSMul","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOUInnovation","GinibrePoincare.ginibreBrownianOUInnovation_hasLaw","GinibrePoincare.ginibreBrownianOUInnovation_independent_value","GinibrePoincare.ginibreBrownianOU_step_ae","GinibrePoincare.ginibreBrownianOU_zero_hasLaw","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.aemeasurable","MeasureTheory.MemLp.const_smul","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","MonoidWithZero.toMulActionWithZero","MonoidWithZero.toMulZeroOneClass","MulActionWithZero.toSMulWithZero","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Or","Pi.instAdd","ProbabilityTheory.HasGaussianLaw.memLp_two","ProbabilityTheory.HasLaw.hasGaussianLaw","ProbabilityTheory.HasLaw.variance_eq","ProbabilityTheory.IndepFun.covariance_eq_zero","ProbabilityTheory.IndepFun.symm","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsGaussian","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.covariance","ProbabilityTheory.covariance_add_right","ProbabilityTheory.covariance_self","ProbabilityTheory.covariance_smul_right","ProbabilityTheory.gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","ProbabilityTheory.variance","ProbabilityTheory.variance_id_gaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCompleteSpace","Real.instIsDomain","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring.toSemiring","SMulWithZero.toSMulZeroClass","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoidWithZero","Set","Set.instMembership","Set.ofPred","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congrArg","congrFun'","id","inferInstance","instHAdd","instHMul","instHSMul","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","mul_eq_mul_left_iff._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUConvolution","name":"GinibrePoincare.ginibreBrownianOU_zero_hasLaw","type_dependencies":["DFunLike.coe","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreOUTransition","MeasurableSpace","MeasureTheory.Measure","NNReal","NNReal.toReal","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","Real","Real.instZero","Real.measurableSpace","Real.sqrt","Zero.toOfNat0"],"value_dependencies":["DFunLike.coe","Eq","Eq.mpr","Eq.refl","Filter.atTop","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOURiemannSum","GinibrePoincare.ginibreBrownianOURiemannSum_ae_tendsto","GinibrePoincare.ginibreBrownianOURiemannSum_hasLaw","GinibrePoincare.ginibreBrownianOURiemannVariance","GinibrePoincare.ginibreBrownianOURiemannVariance_tendsto","GinibrePoincare.ginibreGaussian_hasLaw_of_ae_limit","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","HMul.hMul","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.toReal","Nat","Nat.instPreorder","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Rea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o","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Real.toNNReal","Real.toNNReal_le_iff_le_coe","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","Set.ofPred","Set.uIcc","Set.uIcc_of_le","StarOrderedRing.toIsOrderedRing","Subtype.val","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementGlobal.0.GinibrePoincare.ginibreBrownian_center_Lamperti_positive_start_fixed._proof_1_1","bot_le","cast","congrArg","dite","div_pos","gt_mem_nhds","id","instAddNat","instArchimedeanNat","instCommCStarAlgebraComplex","instCommSemiringNNRat","instCountableNat","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHSub","instInhabitedNat","instIsDirectedOrder","instLENat","instLTNat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","intervalIntegral","intervalIntegral.integral_congr","le_add_of_nonneg_right","le_rfl","min_eq_left","nhds","normedAlgebraRat","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementLocal","name":"GinibrePoincare.ginibreBrownian_center_Lamperti_positive_start_local","type_dependencies":["And","Distrib.toAdd","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","EuclideanSpace","Filter.Eventually","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUnitShiftedUniformSum","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreCenterRadialDirection","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreSquareRootCenter","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.sqrt","Real.toNNReal","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHSub","instLENat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddM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ianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreHamiltonian","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.real","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instSub","Real.instZero","Real.log","Real.measurableSpace","Set.ofPred","WithTop.some","Zero.toOfNat0","instHAdd","instHDiv","instHMul","instHSub","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.addLeftReflectLE_of_addLeftMono","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyLE","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess_range","GinibrePoincare.ginibreBrownian_center_barrier_stopped_expectation","GinibrePoincare.ginibreCenterLogBarrier","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreCenterSquared_nonneg","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianSublevel","GinibrePoincare.ginibreHamiltonianSublevel_centerSquared_bound","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toMulPosStrictMono","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.neg_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le",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brePoincare.ginibreBrownianMaximalLifetime_top_ae","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownian_stopped_compact_test_expectation","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_eventually_eq_cap","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_le","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.hasCompactSupport_ginibrePregenerator","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.exists_bound_of_continuous","HasCompactSupport.mul_left","HasSolidNorm.orderClosedTopology","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.natCast_nonneg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.Integrable.aestronglyMeasurable","MeasureTheory.Integrable.mono'","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.StronglyMeasurable.mono","MeasureTheory.ae","MeasureTheory.ae_all_iff","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.tendsto_integral_of_dominated_convergence","Membership.mem","MetricSpace.toEMetricSpace","Min.min","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instCommSemiring","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","OrderTopology.of_linearLocallyFinite","PartialOrder.toPreorder","Pi.borelSpace","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instArchimedean",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asurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NNReal","NNReal.toReal","Nat","Neg.neg","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.toNNReal","Set.Ioi","Zero.toOfNat0","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddMonoid.toAddZeroClass","And","And.left","And.right","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Compl.compl","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.continuous","Continuous","Continuous.const_mul","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Fin","Fin.fintype","GE.ge","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.boundedDuhamel_laplace_core","GinibrePoincare.collisionSet","GinibrePoincare.continuous_ginibrePregenerator_of_core","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownian_bounded_continuous_transition_mean_continuous","GinibrePoincare.ginibreBrownian_core_test_transition_duhamel","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.hasCompactSupport_ginibrePregenerator","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.exists_bound_of_continuous","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.real","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.norm_integral_le_of_norm_le_const","MeasureTheory.probReal_univ","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Neg.neg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.coe_toNNReal","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAdd","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.lattice","Real.measurableSpace","Real.measureSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_zero","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Ioi","Set.instCompl","Set.instLE","Set.univ","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","abs","add_zero","congrArg","congrFun'","funext","id","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instTopENat","intervalIntegral","intervalIntegral.integral_same","mul_one","tsupport"]},{"kind":"theorem","module":"Gi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eminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.instSub","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instHAdd","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AEMeasurable.aestronglyMeasurable","AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","Bool","Bool.true","BorelSpace.opensMeasurable","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm","ContinuousENorm.toENorm","ContinuousMul.measurableMul\u2082","Distrib.toAdd","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Function.comp","GinibrePoincare.ginibreBrownian_family_distinct_increment_independent","GinibrePoincare.ginibreBrownian_increment_hasLaw","GinibrePoincare.ginibreGaussian_hasLaw_square_memLp_two","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Measurable.pow_const","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable.mul","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.memLp_two_iff_integrable_sq","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.addLeftMono","NNReal.addLeftReflectLT","NNReal.instAddCancelCommMonoid","NNReal.instOrderBot","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.instZero","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instMeasurableSpace","Nat.instNeZeroSucc","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instMul","Preorder.toLE","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.integrable_mul","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instCommMonoid","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","TopologicalSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_tsub_cancel_left","autoParam","bot_le","congrArg","congrFun'","eq_of_heq","funext","id","instDistribOfSemiring","instENormSMulClass","instHAdd","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","le_add_of_nonneg_right","measurable_id","mul_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedMoments","name":"GinibrePoincare.ginibreBrownian_family_mixed_increment_secondMoment","type_dependencies":["Distrib.toAdd","Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub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","MeasureTheory.integral","Membership.mem","NNReal","NNReal.toReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreFullRealPaperEvolution","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","GinibrePoincare.ginibreOriginalStochasticL2Operator_bounded_representative","GinibrePoincare.ginibreOriginalSymmetricStochasticL2Operator","GinibrePoincare.ginibreOriginalSymmetricStochasticL2Operator_eq_paper","GinibrePoincare.ginibreStationaryContinuousTransitionMean","GinibrePoincare.ginibreStationaryContinuousTransitionMean_eq_original","GinibrePoincare.ginibre_ae_collisionFree","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Real.toNNReal","Real.toNNReal_coe","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","funext","id","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticBrownianPlanarCrossConditional","name":"GinibrePoincare.ginibreBrownian_planar_cross_predictable_conditional","type_dependencies":["Distrib.toAdd","Filter.EventuallyEq","GinibrePoincare.ginibrePlanarBrownianPastMeasurableSpace","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.condExp","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Prod","Prod.instMeasurableSpace","Prod.mk","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHSub"],"value_dependencies":["AEMeasurable","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousMul.measurableMul\u2082","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Filter.Eventually.of_forall","Function.comp","GinibrePoincare.ginibreBrownian_planar_increment_hasLaw","GinibrePoincare.ginibreBrownian_planar_increment_independent_past","GinibrePoincare.ginibreIndependent_predictable_centered_conditional","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","Measurable.fst","Measurable.fun_mul","Measurable.prodMk","Measurable.snd","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.mono'","MeasureTheory.Integrable.mul_prod","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsProbabilityMeasure","MeasureTheory.ae","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_prod_mul","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussian.integrable_id","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","ProbabilityTheory.integral_id_gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instInhabited","Real.instLE","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.Elem","Set.Iic","Set.instMembership","StandardBo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ibre_independent_blocks_recombine","HAdd.hAdd","HSub.hSub","Iff.mp","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsTopologicalAddGroup.to_continuousSub","LE.le","Measurable","Measurable.aemeasurable","Measurable.fun_sub","Measurable.of_eval","Measurable.prodMk","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","MeasureTheory.instIsProbabilityMeasureMap","Membership.mem","NNReal","NNReal.addLeftMono","NNReal.addLeftReflectLT","NNReal.instAddCancelCommMonoid","NNReal.instOrderBot","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.instZero","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.IsGaussianProcess.isProbabilityMeasure","ProbabilityTheory.IsPreBrownianReal.aemeasurable","ProbabilityTheory.IsPreBrownianReal.isGaussianProcess","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instAddGroup","Real.instSub","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_tsub_cancel_left","aemeasurable_iff_measurable","autoParam","bot_le","congrArg","congrFun'","inferInstance","instDistribOfSemiring","instHAdd","instHSub","instIsTopologicalAddGroupReal","instSecondCountableTopologyReal","le_add_of_nonneg_right","measurable_pi_apply","measurable_pi_lambda","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticBrownianPlanarPredictableSquare","name":"GinibrePoincare.ginibreBrownian_planar_predictable_cross_secondMoment","type_dependencies":["Distrib.toAdd","Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Prod","Prod.instMeasurableSpace","Prod.mk","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.measurableSpace","Real.normedAddCommGroup","Set","Set.Elem","Set.Iic","Set.instMembership","Subtype.val","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatNat"],"value_dependencies":["AEMeasurable","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousMul.measurableMul\u2082","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.ginibreBrownian_planar_increment_hasLaw","GinibrePoincare.ginibreBrownian_planar_increment_independent_past","GinibrePoincare.ginibreGaussian_secondMoment","GinibrePoincare.ginibreIndependent_predictable_secondMoment","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.zero_natPow","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tact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ibreDrivenHamiltonianBoundedStop_le","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreRealPaperSpeedGenerator","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.exists_bound_of_continuous","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.Integrable","MeasureTheory.Integrable.add","MeasureTheory.Integrable.congr","MeasureTheory.Integrable.mono'","MeasureTheory.Integrable.sub","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.real","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.StronglyMeasurable.mono","MeasureTheory.ae","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_add","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const","MeasureTheory.integral_zero","MeasureTheory.probReal_univ","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedSpace.toModule","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.borelSpace","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instCompleteSpace","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.to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","PiLp.innerProductSpace._proof_1","Preorder.toLT","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.congr","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instSub","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithLp.ofLp","Zero.toOfNat0","id","instAddNat","instDistribOfSemiring","instFintypeProd","instHAdd","instHSub","instLENat","instOfNatAtLeastTwo","instOfNatNat","measurable_id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticBrownianSums","name":"GinibrePoincare.ginibreBrownian_weighted_increments_hasLaw","type_dependencies":["CommRing.toNonUnitalCommRing","Distrib.toMul","Fin","Fin.castSucc","Fin.fintype","Fin.instPartialOrder","Fin.succ","Finset.sum","Finset.univ","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","MeasurableSpace","MeasureTheory.Measure","Monoid.toNPow","Monotone","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.mk","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.HasLaw","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.gaussianReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instMul","Real.instPreorder","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.semiring","Semiring.toAddCommMonoid","Semiring.toMonoid","StarOrderedRing.toExistsAddOfLE","Zero.toOfNat0","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instOfNatNat","instStarRingReal","sq_nonneg"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.true","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousMul.measurableMul","DFunLike.coe","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Fin","Fin.castSucc","Fin.castSucc_lt_succ","Fin.fintype","Fin.instPartialOrder","Fin.succ","Finset","Finset.instSetLike","Finset.sum","Finset.sum_apply","Finset.sum_congr","Finset.sum_eq_zero","Finset.univ","Function.comp","GinibrePoincare.ginibreBrownian_increment_hasLaw","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LT.lt.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Measurable.const_mul","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_finsetSum","Membership.mem","Monoid.toNPow","Monotone","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.coe_sum","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGr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imalProcess_zero_speed_constant","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.pairwiseRadius","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","NNReal","Nat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","Not","OfNat.ofNat","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun.indepFun","Prod","Prod.mk","Prod.mk.injEq","Real","Real.instZero","Real.measurableSpace","Set","Set.instMembership","Set.ofPred","True","Zero.toOfNat0","and_false","congr","congrArg","eq_self","id","instLTNat","instOfNatNat","not_false_eq_true","of_eq_true","rfl","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticZeroSpeed","name":"GinibrePoincare.ginibreBrownian_zero_speed_transition_integral","type_dependencies":["Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.integral","NNReal","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.trans","Filter.Eventually.mono","Filter.EventuallyEq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownianMaximalProcess_zero_speed_constant","HSMul.hSMul","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.real","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const","MeasureTheory.probReal_univ","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instMonoid","Real.instOne","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.semiring","SMulZeroClass.toSMul","Set.univ","SubNegMonoid.toAddMonoid","True","Zero.toOfNat0","congrArg","congrFun'","eq_self","id","instHSMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat","of_eq_true","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterZeroSpeed","name":"GinibrePoincare.ginibreBrownian_zero_speed_two_radius_CIR_realization","type_dependencies":["And","Continuous","DivInvMonoid.toDiv","Eq","Exists","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreBrownianHamiltonianBoundedStop","GinibrePoincare.ginibreBrownianHamiltonianStoppedProcess","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddComm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oMetricSpace","Subtype","Subtype.instMeasurableSpace","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","measurable_prodMk_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianTransitionKernel","name":"GinibrePoincare.ginibreCanonicalTransitionKernel_isMarkov","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreCanonicalTransitionKernel","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","LT.lt","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","NNReal","Nat","OfNat.ofNat","ProbabilityTheory.IsMarkovKernel","Real","Subtype","Subtype.instMeasurableSpace","instLTNat","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","Complex.measurableSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreCanonicalTransitionKernel","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreDrivenMaximalValue_joint_measurable","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","LT.lt","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","NNReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","ProbabilityTheory.IsMarkovKernel","ProbabilityTheory.Kernel.IsMarkovKernel.map","ProbabilityTheory.Kernel.IsMarkovKernel.prod","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.const.instIsMarkovKernel","ProbabilityTheory.Kernel.id","ProbabilityTheory.Kernel.instIsMarkovKernelId","ProbabilityTheory.Kernel.prod","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","Subtype.instMeasurableSpace","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","id","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreCollisionCapacity","name":"GinibrePoincare.ginibreCapacity","type_dependencies":["GinibrePoincare.Configuration","Nat","Real","Set"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.ginibreCapacityCosts","InfSet.sInf","Nat","Real","Real.instInfSet","Set"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryCapacitySpeed","name":"GinibrePoincare.ginibreCapacityAtSpeed","type_dependencies":["GinibrePoincare.Configuration","Nat","Real","Set"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.ginibreCapacityCostsAtSpeed","InfSet.sInf","Nat","Real","Real.instInfSet","Set"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreCollisionCapacity","name":"GinibrePoincare.ginibreCapacityCosts","type_dependencies":["GinibrePoincare.Configuration","Nat","Real","Set"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreCapacityCosts._proof_1","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsOpen","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlg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inormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","mul_nonneg","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterLampertiNoiseCoefficient","name":"GinibrePoincare.ginibreCenterCIR_noise_amplitude_factor","type_dependencies":["DivInvMonoid.toDiv","Eq","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquared","HDiv.hDiv","HMul.hMul","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instZero","Real.sqrt","Zero.toOfNat0","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquared","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","IsOrderedRing.toPosMulMono","LE.le","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_realSqrt","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_mul","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","True","True.intro","Zero.toOfNat0","congrArg","congrFun'","eq_self","eq_true","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_nonneg","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterCIRNoiseCoefficient","name":"GinibrePoincare.ginibreCenterCIR_noise_amplitude_square","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreRepeatedCenterCLM","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instZero","Real.norm","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Decidable.decide","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreRepeatedCenterCLM","GinibrePoincare.ginibreRepeatedCenterEuclidean_norm_sq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit1","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_ofNat","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.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roSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRadialCenterIndependence","name":"GinibrePoincare.ginibreCenterOUValue.eq_1","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","DivInvMonoid.toDiv","Eq","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.drivenOUPath","GinibrePoincare.ginibreCenterOUValue","GinibrePoincare.ginibreCenterOUValue._proof_1","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","NNReal","NNReal.toReal","Nat","Nat.cast","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHDiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterOUValue","NNReal","Nat","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianCenterFunctional","name":"GinibrePoincare.ginibreCenterOUValue_measurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","ContinuousMap","ContinuousMap.compactOpen","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterOUValue","Measurable","NNReal","Nat","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","borel","instCommCStarAlgebraComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.algebraMap","Algebra.toSMul","BorelSpace.mk","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","Continuous","Continuous.comp","Continuous.measurable","Continuous.mul","Continuous.smul","ContinuousAdd.measurableMul\u2082","ContinuousEval.continuous_eval","ContinuousEvalConst.continuous_eval_const","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousEvalConst","ContinuousMap.instContinuousEvalOfLocallyCompactPair","ContinuousMap.instFunLike","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub\u2082","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.drivenOUCorrection","GinibrePoincare.ginibreCenterOUValue._proof_1","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.add","Measurable.smul","Measurable.stronglyMeasurable","Measurable.sub","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.StronglyMeasurable","MeasureTheory.StronglyMeasurable.integral_prod_right'","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.instSFiniteRestrict","MeasureTheory.integral","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Module.toMulActionWithZero","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom.toZeroHom","MulActionWithZero.toSMulWithZero","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNR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ibrePoincare.ginibreCenterPositiveStart","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","Inv.inv","IsScalarTower.nnrat","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.coe_natCast","NNReal.instOne","NNReal.instSemifield","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.tendsto_coe","NNReal.toReal","Nat","Nat.cast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","funext","id","instCommSemiringNNRat","instDistribOfSemiring","instHAdd","instHDiv","instMulZeroClassOfSemiring","nhds","normedAlgebraRat","one_div","propext","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionCLM","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Fin","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","DistribMulAction.toDistribSMul","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","GinibrePoincare.ginibreCenterProjectionCLM._proof_1","GinibrePoincare.ginibreCenterProjectionCLM._proof_2","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionCLM._proof_1","type_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedField","DistribMulAction.toMulAction","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instCommMonoid","Real.instRCLike","Real.normedField","Real.semiring","SMulCommClass","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedField","DistribMulAction.toMulAction","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instCommMonoid","Real.instRCLike","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionCLM._proof_2","type_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformContinuousConstSMul.instContinuousConstSMul","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionCLM.eq_1","type_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","DistribMulAction.toDistribSMul","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","GinibrePoincare.ginibreCenterProjectionCLM","GinibrePoincare.ginibreCenterProjectionCLM._proof_1","GinibrePoincare.ginibreCenterProjectionCLM._proof_2","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterProjectionCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionCLM_apply","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterProjectionCLM","GinibrePoincare.projectToCenterLine","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","Algebra.toSMul","CommMagma.toMul","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.ofReal","Complex.ofReal_inv","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DistribMulAction.toDistribSMul","DivInvMonoid.toInv","DivInvMonoid.toMonoid","Eq","Eq.trans","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","GinibrePoincare.ginibreCenterProjectionCLM","GinibrePoincare.ginibreCenterProjectionCLM._proof_1","GinibrePoincare.ginibreCenterProjectionCLM._proof_2","GinibrePoincare.projectToCenterLine","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","congr","congrArg","congrFun'","div_eq_mul_inv","eq_self","funext","instHMul","instHSMul","instInnerProductSpaceRealComplex","mul_comm","of_eq_true","smul_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterProjectionEuclidean","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv.symm","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap.comp","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.ginibreCenterProjectionCLM","GinibrePoincare.ginibreCenterProjectionEuclidean._proof_1"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oid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.normSq","Continuous.comp","Continuous.continuousAt","ContinuousAt","ContinuousAt.comp","ContinuousLinearEquiv","ContinuousLinearEquiv.continuous","ContinuousLinearEquiv.continuousSemilinearEquivClass","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.injective","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousSemilinearEquivClass.continuousSemilinearMapClass","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EmbeddingLike.map_eq_zero_iff._simp_1","Eq","Eq.mp","Eq.mpr","Eq.trans","EquivLike.toEmbeddingLike","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Fin.mk","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.brownianRadialUnitVector","GinibrePoincare.brownianRadialUnitVector_continuousAt","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM_apply","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreRepeatedCenterCLM","InnerProductSpace.toNormedSpace","LT.lt","Module.toDistribMulAction","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toZeroHomClass","Nat","Ne","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.instZero","Pi.topologicalSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instCompleteSpace","Real.instRCLike","Real.instRing","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","congrArg","congrFun","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","map_zero","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterDirection","name":"GinibrePoincare.ginibreCenterRadialDirection_measurable","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterRadialDirection","Measurable","MeasurableSpace.pi","Nat","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","Real","Real.measurableSpace","WithLp.measurableSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous.measurable","ContinuousLinearEquiv","ContinuousLinearEquiv.continuous","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.measurable","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.brownianRadialUnitVector","GinibrePoincare.brownianRadialUnitVector_measurable","GinibrePoincare.configurationEuclideanEquiv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eCenterRadialDirection_scaled_coordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreCenterRadialDirection","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreRepeatedCenterCLM","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instRing","Real.instZero","Real.norm","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","Zero.toOfNat0","instCommCStarAlgebraComplex","instFintypeProd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","Classical.propDecidable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Decidable","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toInv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.ginibreCenterRadialDirection","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreRepeatedCenterCLM","GinibrePoincare.ginibreRepeatedCenterEuclidean_norm_sq","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Inv.inv","LT.lt","LT.lt.ne'","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instCharZero","Nat.instPreorder","Ne","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Or","Or.resolve_left","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instField","Real.instFloorRing","Real.instInv","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instSemigroup","Real.instZero","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","Semigroup.toMul","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","Zero.toOfNat0","cast","congrArg","congrFun","congrFun'","fact_one_le_two_ennreal","id","if_neg","instCommCStarAlgebraComplex","instFintypeProd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_assoc","mul_eq_zero","mul_inv_cancel\u2080","norm_ne_zero_iff","norm_zero","one_mul","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreCenterRecenterEuclidean_orthogonal","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Fin.fintype","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.ginibreCenterProjectionEuclidean","GinibrePoincare.ginibreRecenterProjectionEuclidean","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.instZero","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.ginibreCenterProjectionEuclidean","GinibrePoincare.ginibreCenterProjectionEuclidean_recenter_zero","GinibrePoincare.ginibreCenterProjectionEuclidean_selfAdjoint","GinibrePoincare.ginibreRecenterProjectionEuclidean","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.instZero","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","inner_zero_right","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementLocalization","name":"GinibrePoincare.ginibreCenterRegularizedIto_positive_start_increment","type_dependencies":["Eq","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquareRootRegularized","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.ginibreSquareRootCenter","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IntervalIntegrable","LE.le","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instLT","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.toNNReal","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSub","instLENat","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And.intro","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterRegularized_generator_interval","GinibrePoincare.ginibreCenterSquareRootRegularized","GinibrePoincare.ginibreCenterSquareRootRegularized_eq","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.ginibreSquareRootCenter","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IntervalIntegrable","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_eq_of_eq","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","Not.intro","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instLT","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measureSpace","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toSub",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nAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2._proof_4","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2._proof_1","GinibrePoincare.ginibreCenterSumL2._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreCenterSumL2._proof_1","GinibrePoincare.ginibreCenterSumL2._proof_2","GinibrePoincare.ginibreCenterSumL2._proof_3","GinibrePoincare.ginibreCenterSumL2._proof_5","GinibrePoincare.ginibreCenterSumL2._proof_6","GinibrePoincare.ginibreCoordinateSumPowerL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.mp","Field.toDivisionRing","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreCoordinateSumPowerL2","GinibrePoincare.ginibreCoordinateSumPowerL2_ae","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","funext","id","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","pow_one"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2_conjugateProjection_zero","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.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easureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonAssocSemiring.toMulZeroOneClass","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","Submodule","Submodule.eq_starProjection_of_mem_of_inner_eq_zero","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Submodule.starProjection_apply_mem","Submodule.starProjection_eq_self_iff","Submodule.starProjection_inner_eq_zero","Submodule.zero_mem","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congrArg","fact_one_le_two_ennreal","id","inner_add_right","inner_conj_symm","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","map_zero","starRingEnd","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2_constantProjection_zero","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","No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oincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreCoordinateSumPowerL2","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMassEvaluation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_coeFn_public","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.polynomialVandermonde","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeSymmetricAlternatingEquiv","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearEquiv.toLinearMap","LinearIsometry","LinearIsometry.instFunLike","LinearIsometryEquiv","LinearIsometryEquiv.injective","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.toLinearEquiv","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_X","Nat","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomInvPair.ids","RingHomSurjective.ids","SMulZeroClass.toSMul","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.coe","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.comap","Submodule.le_topologicalClosure","Submodule.map","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smul_mem","Submodule.subtype","Subtype","Subtype.val","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","congr","congrArg","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","map_mul","map_sum","mul_assoc","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCenterSumL2_mem_phase_one","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreHolomorphicPhaseDegree","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finset.mul_sum","Finset.sum","Finset.univ","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreCenterSumL2_ae","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreGlobalPhaseL2","GinibrePoincare.ginibreHolomorphicPhaseDegree._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.globalPhase","GinibrePoincare.measurePreserving_globalPhase_ginibreMeasure","HMul.hMul","HPow.hPow","HSMul.hSMul","IsTopologicalAddGroup.toContinuousAdd","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","N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Poincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreHolomorphicProjection_split","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","HAdd.hAdd","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Submodule.starProjection_apply_mem","Submodule.starProjection_eq_self_iff","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHAdd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","zero_add"]},{"kind":"definition","module":"GinibrePoincare.Endgame.FullTheoremOneNine","name":"GinibrePoincare.ginibreCenteredHermiteMass","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreCenteredHermiteMass._proof_1","GinibrePoincare.ginibreFullCenteredTransform","GinibrePoincare.ginibreMeasure","GinibrePoincare.positiveHermiteModeMass","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.FullTheoremOneNine","name":"GinibrePoincare.ginibreCenteredHermiteMass._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadratic","type_dependencies":["Complex","GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.recenteredConfiguration","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","OfNat.ofNat","Semiring.toMonoid","instHPow","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadraticL2","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.ginibreMeasure","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.ginibreCenteredQuadratic","GinibrePoincare.ginibreCenteredQuadratic_memLp","GinibrePoincare.ginibreMeasure","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp.toLp","Nat","OfNat.ofNat","instLENat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadraticL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.ginibreCenteredQuadraticL2","GinibrePoincare.ginibreMeasure","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLENat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.ginibreCenteredQuadraticL2","GinibrePoincare.ginibreMeasure","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLENat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadraticL2_inner","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.ginibreCenteredQuadratic","GinibrePoincare.ginibreCenteredQuadraticL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunctionL2","HMul.hMul","Inner.inner","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.integral","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instRCLike","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex","instLENat","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","ENNReal","ENNRe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Poincare.ginibreCenteredQuadratic_memLp","GinibrePoincare.ginibreCenteredQuadratic_not_identically_zero","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_ae_eq_iff_volume","Iff.mp","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_zero","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsOpenPosMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.PolynomialSectorIncompleteness.0.GinibrePoincare.ginibreCenteredQuadraticL2_ne_zero._proof_1_1","congrArg","continuous_const","id","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadraticL2_orthogonal","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreCenteredQuadraticL2","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Submodule","Submodule.orthogonal","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Decidable.byContradiction","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.ginibreCenteredQuadraticL2_orthogonal_of_integrals","GinibrePoincare.ginibreCenteredQuadratic_orthogonal_polynomial","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunction_isPolynomial","LE.le","LT.lt","Nat","Nat.decLt","Not","OfNat.ofNat","_private.GinibrePoincare.Analysis.PolynomialSectorIncompleteness.0.GinibrePoincare.ginibreCenteredQuadraticL2_orthogonal._proof_1_1","instLENat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorIncompleteness","name":"GinibrePoincare.ginibreCenteredQuadraticL2_orthogonal_of_integrals","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.t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emiring","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Fin","FiniteDimensional.rclike_to_real","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreCollisionCutoff","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.vandermondeWeight","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Nat","Nat.cast","Neg.neg","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace._proof_1","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithLp.instSMul","Zero.toOfNat0","deriv","instHAdd","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.differentiable","ContDiffBump.contDiff","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.sub","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.differentiableAt","DifferentiableAt.hasDerivAt","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.comp","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.ginibreCollisionCutoff","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_coordinate","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.vandermondeWeight","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasDerivAt.comp_hasFDerivAt","HasDistribNeg.toInvolutiveNeg","HasFDerivAt","HasFDerivAt.const_mul","HasFDerivAt.fderiv","HasFDerivAt.sub","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocComm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","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompl","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","congr","congrArg","congrFun'","eq_self","id","instHMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instTopENat","of_eq_true","tsupport","tsupport_mul_subset_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCollisionCutoff","name":"GinibrePoincare.ginibreCollisionCutoff_smooth","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreCollisionCutoff","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.comp","ContDiff.mul","ContDiff.sub","ContDiffBump.contDiff","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","ENat","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.ginibreCollisionCutoff._proof_1","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.vandermondeWeight","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","Zero.toOfNat0","contDiff_const","instHAdd","instHMul","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCollisionCutoffSobolevApproximation","name":"GinibrePoincare.ginibreCollisionCutoff_smoothPair_core_sequence","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreTheoremOneNineCorePairs","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Sem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orm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instSMul","WithTop.some","Zero.toOfNat0","add_zero","congrArg","eq_self","fact_one_le_two_ennreal","id","instCountableFin","instFintypeProd","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSMulOfMul","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopENat","instTopologicalSpaceProd","le_trans","nhds","norm_nonneg","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCollisionCutoffSobolevApproximation","name":"GinibrePoincare.ginibreCollisionCutoff_smoothPair_core_sequence_of_smoothCompact","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreTheoremOneNineCorePairs","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","And.left","And.right","Classical.propDecidable","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.continuous","Continuous.continuousOn","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.trans","EuclideanSpace","Exists","Exists.casesOn","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreCollisionCutoff_smoothPair_core_sequence","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreTheoremOneNineCorePairs","HasCompactSupport","InnerProductSpace.toNormedSpace","IsCompact.exists_bound_of_continuousOn","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Preorder.toLE","Pro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riviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithTop","WithTop.natCast","Zero.toOfNat0","fderiv","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.left","And.right","Classical.choose","Classical.choose_spec","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","ContDiffOn","Continuous","Continuous.continuousOn","Continuous.mul","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousOn","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","EDist","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toAddCommMonoid","EmptyCollection.emptyCollection","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Filter","Filter.Eventually","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finset","Finset.induction_on","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.sum","Finset.sum_apply","Finset.sum_congr","Finset.sum_const_zero","Finset.sum_insert","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.brownianContinuousIntegral_exists","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.brownianUniformPartialSum_memLp_two","GinibrePoincare.brownianUniformPartialSum_terminal","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreCompactProcess_test_coefficients","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationBrownianGradientSum_eq","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibre_tendstoInMeasure_const_mul","GinibrePoincare.itoConfigurationHessianEntry","GinibrePoincare.itoTendstoInMeasure_finset_sum","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Insert.insert","IsCompact","IsOpen","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Martingale.add","MeasureTheory.Martingale.smul","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.MemLp.const_mul","MeasureTheory.MemLp.of_bound","MeasureTheory.StronglyAdapted","MeasureTheory.StronglyMeasurable.aestronglyMeasurable","MeasureTheory.StronglyMeasurable.measurable","MeasureT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uousLinearMap","ContinuousLinearMap.funLike","ContinuousOn","ContinuousOn.comp_continuous","ContinuousOn.mono","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreCompactProcess_scalar_stronglyAdapted","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.itoConfigurationCoefficients_exists_bound","GinibrePoincare.itoConfigurationGradientEntry_continuousOn","GinibrePoincare.itoConfigurationHessianEntry","GinibrePoincare.itoConfigurationHessianEntry_continuousOn","InnerProductSpace.toNormedSpace","IsCompact","IsOpen","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.StronglyAdapted","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instRCLike","Real.instZero","Real.norm","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fderiv","inferInstance","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreRadialWeakSobolevApproximation","name":"GinibrePoincare.ginibreCompactRadialWeakSobolevPairs","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreRadialL2Value._proof_1","GinibrePoincare.IsGinibreRadialL2Value._proof_2","GinibrePoincare.IsGinibreRadialL2Value._proof_3","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRadialWeakSobolevPairs._proof_1","HasCompactSupport","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instMulZeroOneC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NReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreCollisionFreeCompactTest","GinibrePoincare.ginibreCompactTestValue._proof_1","GinibrePoincare.ginibreCompactTestValue._proof_2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp.toLp","Nat","OfNat.ofNat","Real","Real.normedAddCommGroup","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionCompactResolvent","name":"GinibrePoincare.ginibreCompactTestValue._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionCompactResolvent","name":"GinibrePoincare.ginibreCompactTestValue._proof_2","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreCollisionFreeCompactTest","GinibrePoincare.ginibreCompactTestValue._proof_1","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","And","And.left","And.right","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Compl.compl","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff","ContDiff.continuous","Continuous.memLp_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","Finite.of_fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreCollisionFreeCompactTest","GinibrePoincare.collisionSet","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","OfNat.ofNat","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instCompl","Set.instLE","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","WithTop.some","instCommCStarAlgebraComplex","instCountableFin","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSigmaCompactSpaceForallOfFinite","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","secondCountable_of_proper","tsupport"]},{"kind":"theorem","module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oidWithOne.toNatCast","And","And.casesOn","And.intro","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instSub","ContDiffOn","Continuous","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Filter.Eventually","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.atTop","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformPartialSum","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreCompactProcess_continuous_gradient_integral_all_horizons","GinibrePoincare.ginibreCompactVolterra_compensator_eq_gradient_process_until","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationTestCompensator","GinibrePoincare.ginibreCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsCompact","IsOpen","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.StronglyAdapted","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.measurableSpace","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toNorm","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedRing","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instMembership","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithTop","WithTop.natCast","Zero.toOfNat0","fderiv","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCompactItoMartingale","name":"GinibrePoincare.ginibreCompactVolterra_continuous_ito_martingale_exists","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instSub","ContDiffOn","Continuous","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Exists","Filter.Eventually","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationTestCompensator","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IsCompact","IsOpe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roup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithTop","WithTop.natCast","Zero.toOfNat0","add_zero","aemeasurable_iff_measurable","congrArg","funext","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instCommSemiringNNRat","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instStarRingReal","intervalIntegral","measurable_const","nhds","normedAlgebraRat","pi_properSpace","rfl","sq_nonneg","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCompactDerivativeMeasurability","name":"GinibrePoincare.ginibreCompact_fderiv_apply_measurable","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiffOn","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","IsOpen","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fderiv","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddUnits","Bool","Bool.true","BorelSpace.opensMeasurable","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiffOn","ContDiffOn.continuousOn_fderiv_of_isOpen","Continuous.clm_apply","Continuous.measurable","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instBorelSpace","ContinuousLinearMap.instMeasurableSpace","ContinuousLinearMap.topologicalSpace","ContinuousOn.mono","ContinuousOn.restrict","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.instNatCast","Eq.refl","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","IsOpen","LE.le","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Measurable","Measurable.comp","Measurable.prodMk","Measurable.subtype_mk","MeasurableSpace","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSemi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ibrePoincare.ginibreComplexPairRe._proof_4","GinibrePoincare.ginibreComplexPairRe._proof_5","GinibrePoincare.ginibreComplexPairRe._proof_6","GinibrePoincare.ginibreComplexPairRe._proof_7","GinibrePoincare.ginibreComplexPairRe._proof_9","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.instAdd","Prod.instAddCommMonoid","Prod.instModule","Prod.instSMul","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.ginibreComplexPairCombine._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreComplexGradientPair._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreComplexGradientPair._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.ginibreComplexPairCombine._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMon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GinibrePoincare.ginibreComplexRealProdEquiv","type_dependencies":["Complex","Complex.measurableSpace","MeasurableEquiv","Prod","Prod.instMeasurableSpace","Real","Real.measurableSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.equivRealProdCLM","Complex.instAddCommMonoid","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearEquiv.toHomeomorph","GinibrePoincare.ginibreComplexRealProdEquiv._proof_1","Homeomorph.toMeasurableEquiv","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instMeasurableSpace","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUComplexTransition","name":"GinibrePoincare.ginibreComplexRealProdEquiv._proof_1","type_dependencies":["BorelSpace","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instTopologicalSpaceProd"],"value_dependencies":["Prod.borelSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instSecondCountableTopologyReal","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","name":"GinibrePoincare.ginibreComplexSmoothCore_closure_equivalence","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreComplexGradientPair","GinibrePoincare.GinibreComplexGradientPair._proof_1","GinibrePoincare.GinibreComplexGradientPair._proof_2","GinibrePoincare.GinibreComplexGradientSpace","GinibrePoincare.ginibreComplexEuclideanGradient._proof_1","GinibrePoincare.ginibreGlobalComplexSmoothPairs","GinibrePoincare.ginibreInteriorComplexSmoothPairs","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","closure","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.symm","EuclideanSpace","Exists.casesOn","Exists.intro","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreComplexGradientPair","GinibrePoincare.GinibreComplexGradientPair._proof_1","GinibrePoincare.GinibreComplexGradientPair._proof_2","GinibrePoincare.GinibreComplexGradientSpace","GinibrePoincare.GinibreRealGradientPair","GinibrePoincare.GinibreRealGradientPair._proof_1","GinibrePoincare.GinibreRealGradientPair._proof_2","GinibrePoincare.GinibreRealGradientSpace","GinibrePoincare.ginibreComplexEuclideanGradient","GinibrePoincare.ginibreComplexEuclideanGradient._proof_1","GinibrePoincare.ginibreComplexPairCombine","GinibrePoincar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rePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LinearEquiv","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.instSub","Prod","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","instAddNat","instFintypeProd","instHAdd","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticConfigurationHessianSum","name":"GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum.eq_1","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSub","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","Eq","EquivLike.toFunLike","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanLinearEquiv","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LinearEquiv","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.instSub","Prod","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","instAddNat","instFintypeProd","instHAdd","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","NNReal","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticConfigurationHessianSum","name":"GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum_eq","type_dependencies":["DivInvMonoid.toDiv","Eq","Fin","Fin.fintype","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","HDiv.hDiv","HMul.hMul","HPow.hPow","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Prod","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","instFintypeProd","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSub","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.refl","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanLinearEquiv","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationBrownianNoise_increment_coordinate","GinibrePoincare.ginibreUniformBrownianTime","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LinearEquiv","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.coe_nonneg","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.instSub","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Prod","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.linearOrder","Real.normedField","Real.partialOrder","Real.semiring","Real.sq_sqrt","Real.sqrt","Ring.toAddGroupWithOne","RingHom.id","RingHomInvPair.ids","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","True","Zero.toOfNat0","congr","congrArg","congrFun'","div_nonneg","eq_self","instAddNat","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","le_of_lt","mul_nonneg","mul_pow","of_eq_true","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticConfigurationHessianSum","name":"GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum_tendstoInProbability","type_dependencies":["DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","Fin","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","HDiv.hDiv","HMul.hMul","HPow.hPow","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","OfNat.ofNat","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.measurableSpace","Real.metricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","instHDiv","instHMul","instHPow","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EDist","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter","Filter.atTop","Fin","Fin.fintype","Fintype.card","Fintype.card_fin","Fintype.card_prod","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreBrownianFamilyQuadraticSum","GinibrePoincare.ginibreBrownianFamilyQuadraticSum_tendstoInProbability","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum","GinibrePoincare.ginibreConfigurationBrownianCoordinateQuadraticSum_eq","GinibrePoincare.ginibre_tendstoInMeasure_const_mul","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_natCast","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero"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ib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.instSub","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCIRNoiseSums","name":"GinibrePoincare.ginibreConfigurationBrownianGradientSum_radius","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreRecenteredRadialDirection","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","NNReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instZero","Real.sqrt","WithLp.ofLp","Zero.toOfNat0","instAddNat","instFintypeProd","instHAdd","instHDiv","instHMul","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreCIR_noise_coordinate","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationBrownianGradientSum_eq","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreRecenteredRadialDirection","GinibrePoincare.itoUniformNNTime","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Membership.mem","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.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SMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_of_heq","eq_self","funext","inferInstance","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","one_mul","pow_succ_nonneg._simp_1","smul_add","sub_self","sub_zero","zero_add","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticConfigurationBrownianBracket","name":"GinibrePoincare.ginibreConfigurationBrownianNoise_real_square_martingale","type_dependencies":["Complex.re","DivInvMonoid.toDiv","Fin","GinibrePoincare.ginibreBrownianFamilyFiltration","GinibrePoincare.ginibreConfigurationBrownianNoise","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","RCLike.toInnerProductSpaceReal","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.measurableSpace","Real.normedAddCommGroup","inferInstance","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Bool","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero.toDivisionCommMonoid","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addGroupWithOne","Complex.div_natCast_im","Complex.div_natCast_re","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instRCLike","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.ofReal_div","Complex.ofReal_mul","Complex.re","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.hasSMul","GinibrePoincare.ginibreBrownianFamilyFiltration","GinibrePoincare.ginibreBrownianFamilyFiltration_square_martingale","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationBrownianNoise._proof_1","GinibrePoincare.ginibreConfigurationBrownianNoise._proof_2","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","M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at","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.topologicalSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHDiv","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","Continuous.measurable","ContinuousMap","ContinuousMap.comp","ContinuousMap.compactOpen","ContinuousMap.continuous_precomp","ContinuousMap.instSecondCountableTopology","Eq","Eq.mpr","Eq.symm","Eq.trans","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance1","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance2","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance3","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance4","GinibrePoincare.ginibreBrownianOUHorizonPath","GinibrePoincare.ginibreBrownianOUHorizonPath_measurable","GinibrePoincare.ginibreBrownianOU_stationary_continuous_horizon_law_reversal","GinibrePoincare.ginibreConfigurationOUAssemble","GinibrePoincare.ginibreConfigurationOUAssemble_measurable","GinibrePoincare.ginibreConfigurationOUAssemble_reverse","GinibrePoincare.ginibreConfigurationOUReferenceLaw","GinibrePoincare.ginibreHamiltonianCompactReverseTime","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.instMeasurableSpaceContinuousMapElemNNRealIccOfNatReal_ginibrePoincare","HDiv.hDiv","LE.le","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.of_eval","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.Measure.map_map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi_map_pi","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instDiv","NNReal.instOne","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instSecondCountableTopology","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.topologicalSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.hasGaussianLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.isGaussian_gaussianReal","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instPreorder","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","Subtype.pseudoMetricSpace","TopologicalSpace.Subtype.secondCountableTopology","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","congrArg","congrFun'","eq_self","funext","id","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instOfNatAtLeastTwo","instOfNatNat","instPseudoMetricSpaceNNReal","instSecondCountableTopologyReal","instTopologicalSpaceSubtype","locallyCompact_of_proper","measurable_pi_apply","of_eq_true","proper_of_compact"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticRestrictedHessianCorrection","name":"GinibrePoincare.ginibreConfigurationPathHessianSum","type_dependencies":["GinibrePoincare.Configuration","NNReal","Nat","Real"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instSub","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoDirectionalHessian","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","NNReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instAddNat","instCommCStarAlgebraComplex","instHAdd","instHSub","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRestrictedIto","name":"GinibrePoincare.ginibreConfigurationPath_discrete_chain","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","DivInvMonoid.toDiv","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationDriftReconstructionSum","GinibrePoincare.ginibreConfigurationPathHessianSum","GinibrePoincare.itoActualPathTaylorRemainderSum","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","NNReal","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Prod","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreConfigurationDriftReconstructionSum","GinibrePoincare.ginibreConfigurationPathHessianSum","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoActualPathTaylorRemainderSum","GinibrePoincare.itoDirectionalHessian","GinibrePoincare.itoTaylorRemainder","GinibrePoincare.itoUniformPathTaylor_identity","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.addGroup","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.normedField","Real.pseudoMetricSpace","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toAddHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_sub_cancel","congr","congrArg","eq_self","fderiv","id","instAddNat","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatA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CStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiffOn","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreConfigurationTestCompensator","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","HSub.hSub","InnerProductSpace.toNormedSpace","IsOpen","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.toNNReal","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instCommCStarAlgebraComplex","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiffAt.continuousAt","ContDiffOn","ContDiffOn.continuousOn_fderiv_of_isOpen","Continuous","Continuous.clm_apply","Continuous.comp","Continuous.continuousAt","Continuous.intervalIntegrable","Continuous.mul","ContinuousAt","ContinuousAt.comp","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.topologicalSpace","ContinuousOn.comp_continuous","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationLaplacian","GinibrePoincare.ginibreConfigurationTestCompensator","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_contDiffAt","GinibrePoincare.ginibreLangevin_fderiv_generator","GinibrePoincare.ginibreRealPaperSpeedGenerator","GinibrePoincare.itoConfigurationLaplacian_continuousOn","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOpen","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mu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re","GinibrePoincare.normalizedVandermondeL2","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransformL2._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransformL2._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransformL2._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransformL2._proof_4","type_dependencies":["CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.instStarRing","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedRing.toNonUnitalRing","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedStarGroup","StarRing.toStarAddMonoid","instCommCStarAlgebraComplex"],"value_dependencies":["CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.instStarRing","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransformL2.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoid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Eq","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianMeasure_absolutelyContinuous_ginibreMeasure","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreCenterSumL2_ae","GinibrePoincare.ginibreConjugateCenterTransformL2","GinibrePoincare.ginibreMassEvaluation","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_coeFn_public","GinibrePoincare.normalizedVandermondeMultiplier","HMul.hMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_star","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instStarForall","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransform_firstMode","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreConjugateCenterTransformL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule"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CommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.ginibreConjugateCenterTransformL2","GinibrePoincare.ginibreConjugateCenterTransform_norm_sq","GinibrePoincare.ginibreConjugateCenterTransform_zeroMode","GinibrePoincare.normalizedVandermondeGroundStateL2","GinibrePoincare.normalizedVandermondeGroundState_norm_sq","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Inv.inv","LT.lt","LT.lt.ne'","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","NSMul.toSMul","Nat","Nat.cast","Nat.cast_eq_zero._simp_1","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","Nat.instPreorder","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instOne","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_false","eq_self","fact_one_le_two_ennreal","id","instHDiv","instHMul","instHPow","instHSMul","instHSub","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","inv_mul_cancel\u2080","mul_one","norm_zero","not_false_eq_true","nsmul_eq_mul","of_eq_true","one_div","sub_zero","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.ginibreConjugateCenterTransform_higherMode_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.ginibreConjugateCenterTransformL2","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Div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},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreConstantClosedSubspace._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreConstantClosedSubspace._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreConstantClosedSubspace._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantClosedSubspace._proof_2","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreConstantClosedSubspace._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantL2","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","IsClosed","LT.lt","LinearIsometry","Linear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urableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreConstantClosedSubspace_star_mem","GinibrePoincare.ginibreLpStar_involutive","GinibrePoincare.ginibreLpStar_sub","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_inner_star_star","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toSub","Submodule","Submodule.eq_starProjection_of_mem_of_inner_eq_zero","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Submodule.starProjection_apply_mem","Submodule.starProjection_inner_eq_zero","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","star_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexProjectionGeometry","name":"GinibrePoincare.ginibreConstants_le_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instPartialOrder","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","Norm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inibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.degreeZero_orthogonal_positiveGraded","GinibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientDegreeZero_eq_constants","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticContinuousStoppingTime","name":"GinibrePoincare.ginibreContinuousMap_exists_norm_max","type_dependencies":["CompactSpace","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.instNorm","DFunLike.coe","Eq","Exists","Nonempty","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","SeminormedAddCommGroup.toPseudoMetricSpace","TopologicalSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["And","And.casesOn","CompactSpace","Continuous.continuousOn","Continuous.norm","ContinuousMap","ContinuousMap.continuous","Conti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ormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOneParticleSpectrum","name":"GinibrePoincare.ginibreCoordinateSumPowerL2._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateSumPowerL2._proof_2","GinibrePoincare.ginibreCoordinateSumPowerL2._proof_5","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOneParticleSpectrum","name":"GinibrePoincare.ginibreCoordinateSumPowerL2._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreCoordinateSumPowerL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instR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L2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_power_memLp","GinibrePoincare.ginibreMeasure","HPow.hPow","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp.coeFn_toLp","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Semiring.toMonoid","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOneParticleSpectrum","name":"GinibrePoincare.ginibreCoordinateSumPowerL2_norm_sq","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateSumPowerL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.factorial","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Real.instNatCast","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHPow","in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re.Analysis.GinibreDynamicsDrift","name":"GinibrePoincare.ginibreCoulombInteraction","type_dependencies":["GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instSemiring","Complex.instSub","Complex.normSq","Complex.ofReal","DFunLike.coe","DivInvMonoid.toDiv","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","HDiv.hDiv","HSub.hSub","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Real","Real.semiring","instHDiv","instHSub","instMulZeroOneClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPath","name":"GinibrePoincare.ginibreCoulombInteraction.eq_1","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instSemiring","Complex.instSub","Complex.normSq","Complex.ofReal","DFunLike.coe","DivInvMonoid.toDiv","Eq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","HDiv.hDiv","HSub.hSub","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Real","Real.semiring","instHDiv","instHSub","instMulZeroOneClassOfSemiring"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathDriftRegularity","name":"GinibrePoincare.ginibreCoulombInteraction_contDiffAt","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.imCLM","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.normSq","Complex.normSq_eq_zero","Complex.ofReal","Complex.ofRealCLM","Complex.ofReal_ne_zero","Complex.reCLM","ContDiff","ContDiff.add","ContDiff.comp","ContDiff.contDiffAt","ContDiff.mul","ContDiff.sub","ContDiffAt","ContDiffAt.inv","ContDiffAt.mul","ContDiffAt.sum","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","ContinuousLinearMap.proj","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","ENat","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.univ","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","Membership.mem","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toZeroHomClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Ne","NegZeroClass.toZero","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","Pi.instInv","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra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roupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionGeometry","name":"GinibrePoincare.ginibreDivisibleEntireClosedSpace._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionGeometry","name":"GinibrePoincare.ginibreDivisibleEntireClosedSpace_eq_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireClosedSpace","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpa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","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireL2","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreDivisibleEntireL2_eq_holomorphicAmbient","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireL2","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.to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onoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.property","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_nonneg","congrArg","congrFun'","id","inferInstance","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","le_abs_self","le_of_lt","le_of_not_gt","lt_of_not_ge","min_eq_left","neg_neg_of_pos","of_eq_true","rfl","top_le_iff._simp_2"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLocalizationExhaustion","name":"GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_exhausts_of_lifetime_top","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instTop","Eq","Filter.Eventually","Filter.atTop","GinibrePoincare.Configuration","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreHamiltonian","HAdd.hAdd","LE.le","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","Nat","Nat.cast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instNatCast","Semiring.toNonAssocSemiring","Top.top","instHAdd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And","And.casesOn","And.intro","And.right","Bornology.IsBounded.exists_pos_norm_le","CommRing.toRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","Continuous","Distrib.toAdd","Distrib.toMul","ENNReal","ENNReal.coe_le_coe","ENNReal.coe_lt_top._simp_1","ENNReal.instLE","ENNReal.instLinearOrder","ENNReal.instMin","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofNNReal","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Filter.Eventually","Filter.atTop","Filter.eventually_ge_atTop","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","GinibrePoincare.Configuration","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop","GinibrePoincare.ginibreDrivenHamiltonianBoundedStop_coe","GinibrePoincare.ginibreDrivenHamiltonianFirstLevel","GinibrePoincare.ginibreDrivenHamiltonianFirstLevel_le_iff","GinibrePoincare.ginibreDrivenHamiltonianPrefix_continuous","GinibrePoincare.ginibreDrivenLevelHit","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreHamiltonian","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact.image","IsCompact.isBounded","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toMax","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Max.max","Membership.mem","Min.min","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.coe_le_coe","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instLinearOrder","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.cast_le._simp_1","Nat.cast_zero","Nat.instCommSemiring","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSemino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rivenMaximalDomain_eq_Ico_of_finite._simp_1_1","congr","congrArg","id"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianMaximalSegments","name":"GinibrePoincare.ginibreDrivenMaximalLifetime","type_dependencies":["ENNReal","GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","ENNReal","ENNReal.instCompleteLinearOrder","ENNReal.ofNNReal","GinibrePoincare.Configuration","GinibrePoincare.ginibreDrivenHorizons","Membership.mem","NNReal","Nat","Real","Set","Set.Elem","Set.instMembership","Subtype.val","iSup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianMaximalNoiseTopology","name":"GinibrePoincare.ginibreDrivenMaximalLifetime_alive_isOpen","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.instTopologicalSpaceGinibreContinuousNoise","IsOpen","LT.lt","NNReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.ofPred","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instSub","Complex.instZero","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.comp","Continuous.norm","Continuous.sub","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.continuous","ContinuousMap.continuous_restrict","ContinuousMap.instAddGroupOfIsTopologicalAddGroup","ContinuousMap.instFunLike","ContinuousMap.instIsTopologicalAddGroup","ContinuousMap.instNorm","ContinuousMap.instSeminormedAddCommGroup","ContinuousMap.instSubOfContinuousSub","ContinuousMap.norm_coe_le_norm","ContinuousMap.restrict","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Filter","Filter.instMembership","Filter.mem_of_superset","Fin","Fin.fintype","Function.comp","GT.gt","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalLifetime_uniform_noise_neighborhood","GinibrePoincare.instTopologicalSpaceGinibreContinuousNoise","HSub.hSub","HasSolidNorm.orderClosedTopology","IsOpen","IsOpen.mem_nhds","IsTopologicalAddGroup.to_continuousSub","LE.le","LE.le.trans","LT.lt","LT.lt.le","Membership.mem","NNReal","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedRing.toNorm","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommGroup","Pi.addGroup","Pi.instSub","Pi.instZero","Pi.isTopologicalAddGroup","Pi.normedRing","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instIsOrderedAddMonoid","Real.instLE","Real.instLT","Real.instPreorder","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Set.mem_setOf_eq","Set.ofPred","SubNegMonoid.toAddMonoid","Subtype","Subtype.mk","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","compactSpace_Icc","congrArg","congrFun'","continuous_const","continuous_subtype_val","id","instCommCStarAlgebraComplex","instHSub","instHasSolidNormReal","instLTNat","instOfNatNat","instOrderTopologyReal","instTopologicalSpaceSubtype","isOpen_iff_mem_nhds","isOpen_lt","nhds","norm_zero","propext","sub_self"]},{"kind":"theorem","mod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brePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalPath","GinibrePoincare.ginibreDrivenMaximalPath_continuousOn","GinibrePoincare.ginibreDrivenMaximalValue","Iff.mp","Iff.mpr","IsOpen.mem_nhds","LE.le","LT.lt","LT.lt.ne","LT.lt.trans","LT.lt.trans_le","Lattice.toSemilatticeSup","Membership.mem","NNReal","NNReal.coe_nonneg","NNReal.continuous_coe","NNReal.instLinearOrder","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Ne","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","OrderTop.toTop","OrderTopology.to_orderClosedTopology","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_coe","SemilatticeSup.toPartialOrder","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Iio","Set.MapsTo","Set.instMembership","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","exists_between","funext","id","instClosedIciTopology","instDistribLatticeOfLinearOrder","isOpen_Iio","le_top"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianMaximalPath","name":"GinibrePoincare.ginibreDrivenMaximalValue_eq_segment","type_dependencies":["ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real"],"value_dependencies":["And","And.intro","And.left","And.right","Classical.choose","Classical.choose_spec","ENNReal","ENNReal.instLinearOrder","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","Eq.mpr","Eq.symm","Exists","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.GinibreDrivenSegment.eqOn","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalLifetime_exists_segment","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreDrivenMaximalValue._proof_1","LE.le","LT.lt","LT.lt.le","LinearOrder.toDecidableLT","Min.min","NNReal","NNReal.coe_le_coe._simp_1","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.toReal","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.instLE","Real.instPreorder","Real.instZero","SemilatticeInf.toMin","Subtype.property","Zero.toOfNat0","cast","congrArg","dif_pos","dite","id","le_min"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianJointEvaluation","name":"GinibrePoincare.ginibreDrivenMaximalValue_joint_continuousAt_alive","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instZero","ContinuousAt","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.instTopologicalSpaceGinibreContinuousNoise","LT.lt","NNReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","Pi.topologicalSpace","Preorder.toLT","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.right","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instSub","Complex.instZero","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.add","Continuous.comp","Continuous.continuousAt","Continuous.norm","Continuous.sub","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.continuous","ContinuousMap.continuous_restrict","ContinuousMap.instAddGroupOfIsTopologicalAddGroup","ContinuousMap.instFunLike","ContinuousMap.instIsTopologicalAddGroup","ContinuousMap.instNorm","ContinuousMap.instSeminormedAddCommGroup","ContinuousMap.instSubOfContinuousSub","ContinuousMap.norm_coe_le_norm","ContinuousMap.restrict","DFunLike.coe","Dist.dist","DistribLattice.toLattice","ENNReal","ENNReal.instPartialOrder","ENNReal.ofN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al","type_dependencies":["And","CommCStarAlgebra.toNormedCommRing","Complex","Continuous","ENNReal","ENNReal.instTop","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","LE.le","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","And.left","And.right","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Continuous","Continuous.continuousOn","ContinuousOn","Decidable.byContradiction","Distrib.toAdd","ENNReal","ENNReal.coe_le_coe","ENNReal.coe_lt_top._simp_1","ENNReal.coe_toNNReal","ENNReal.instLE","ENNReal.instLinearOrder","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofNNReal","ENNReal.toNNReal","Eq","Eq.mp","Eq.symm","Eq.trans","Exists.intro","False","Fin","Fin.fintype","FloorSemiring.instCharZero","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreDrivenHorizons","GinibrePoincare.ginibreDrivenHorizons_le_lifetime","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreDrivenMaximalValue_eq_segment","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","Iff.mp","InnerProductSpace.toNormedSpace","IntervalIntegrable","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","IsStrictOrderedRing.toIsOrderedCancelAddMonoid","LE.le","LT.lt","LinearOrder.toDecidableEq","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.addLeftMono","NNReal.instFloorSemiring","NNReal.instIsStrictOrderedRing_1","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.toReal","Nat","Ne","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toENormedAddMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instInnerProductSpaceRealComplex","instIsLeftCancelAddOfAddLeftReflectLE","instStarRingNNReal","instZeroLEOneClass","intervalIntegral","le_rfl","lt_add_of_pos_right","not_le_of_gt","of_eq_true","rfl","zero_lt_one"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianCanonicalRestart","name":"GinibrePoincare.ginibreDrivenPath_canonical_restart","type_dependencies":["And","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instSub","Continuous","ENNReal","ENNReal.instTop","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","HAdd.hAdd","HSub.hSub","LE.le","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.instSub","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instLE","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHSub"],"value_dependencies":["AddMonoid.toAddZeroClass","And","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.instSub","Continuous","Continuous.add","Continuous.comp","ENNReal","ENNReal.instTop","Eq","Eq.mp","Fin","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreDrivenMaxi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ow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedAddGroup.to_isIsometricVAdd_right","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","ODE_solution_unique","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addGroup","Pi.complete","Pi.instAdd","Pi.instSub","Pi.isIsometricVAdd''","Pi.isTopologicalAddGroup","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","PolynormableSpace.continuousSMul","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.dist_eq","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.EqOn","Set.Icc","Set.Ici","Set.Ico","Set.Iio","Set.instLE","Set.instMembership","Set.ofPred","Set.uIcc","Set.uIcc_of_le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness.0.GinibrePoincare.ginibreDrivenPath_local_pathwise_unique._abel_1_1","_private.GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness.0.GinibrePoincare.ginibreDrivenPath_local_pathwise_unique._simp_1_3","abs","abs_of_nonneg","congrArg","congrFun'","dist_add_right","eq_of_heq","eq_self","heq_of_eq","id","inferInstance","instAddNat","instClosedIciTopology","instContinuousSMulForall","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instHasSolidNormReal","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","intervalIntegral","intervalIntegral.integral_congr","lipschitzExtensionConstant","lt_of_not_ge","mem_nhdsWithin_of_mem_nhds","nhds","nhdsWithin","of_eq_true","propext","pseudoEMetricSpacePi","pseudoMetricSpacePi","rfl","self_mem_nhdsWithin","sub_add_cancel","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathMeasurableLocalFlow","name":"GinibrePoincare.ginibreDrivenPath_measurable_local_flow","type_dependencies":["And","And.intro","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instFunLike","DFunLike.coe","Eq","Exists","Fin","Fin.fintype","GT.gt","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.drivenBoundedNoiseExtension","GinibrePoincare.drivenBoundedNoiseSpace","GinibrePoincare.drivenSmallNoiseSpace","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","InnerProductSpace.toNormedSpace","LE.le","LT.lt.le","Measurable","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat"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_of_not_gt","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRestart","name":"GinibrePoincare.ginibreDrivenPath_shift","type_dependencies":["Complex","Complex.instSub","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","Pi.instSub","Real","Real.instAdd","Real.instLE","Real.instZero","Zero.toOfNat0","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And.intro","And.left","And.right","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Fin","Fin.fintype","Finite.of_fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IntervalIntegrable","IntervalIntegrable.comp_add_left","IntervalIntegrable.symm","IntervalIntegrable.trans","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Measure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MetricSpace.toEMetricSpace","Min.min","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toENormedAddMonoid","NormedAddGroup.toSeminormedAddGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMin","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.normedField","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathRestart.0.GinibrePoincare.ginibreDrivenPath_shift._abel_1_2","add_sub_cancel_left","add_zero","congr","congrArg","congrFun'","enorm_ne_top","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","intervalIntegral","intervalIntegral.integral_add_adjacent_intervals","intervalIntegral.integral_comp_add_left","le_of_not_gt","rfl","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRestart","name":"GinibrePoincare.ginibreDrivenPath_unique_before_collision","type_dependencies":["Complex","Complex.instNormedField","Continuous","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.EqOn","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","And.left","And.right","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instT2Space","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Continuous","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toSemifield","Filter","Filter.instMembership","Filter.mp_mem","Filter.univ_mem'","Fin","GT.gt","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreDrivenPath_restart_local_unique","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Iio_mem_nhds","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inter.inter","IsClosed","IsClosed.Icc_subset_of_forall_mem_nhdsWithin","IsClosed.inter","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","LinearOrderedSemiField.toDenselyOrdered","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.t2Space","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddMonoid","Real.instCommSemiring","Real.instConditionallyCompleteLinearOrder","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instPreorder","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeSup.toPartialOrder","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ico","Set.Iio","Set.Ioi","Set.instInter","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","inferInstance","instClosedIciTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instMulZeroClassOfSemiring","instOrderTopologyReal","isClosed_Icc","isClosed_eq","lt_of_not_ge","mem_nhdsWithin_of_mem_nhds","nhdsWithin","rfl","self_mem_nhdsWithin"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianJointStability","name":"GinibrePoincare.ginibreDrivenSegment_joint_stability_in_extension","type_dependencies":["Complex","Complex.instNormedField","Complex.instSub","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LipschitzWith","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","Norm.norm","NormedCommRing.toNormedRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedRing.toNorm","OfNat.ofNat","Pi.instSub","Pi.normedRing","Real","Real.exp","Real.instAdd","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Set","Set.EqOn","Set.Icc","Set.instMembership","Zero.toOfNat0","instHAdd","instHMul","instHSub","pseudoEMetricSpacePi"],"value_dependencies":["And","And.intro","And.left","And.right","Complex","Complex.instAdd","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","ContinuousOn","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.drivenVolterra_lipschitz_stability_on","GinibrePoincare.ginibreLangevinDrift","HAdd","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IntervalIntegrable","LE.le","LE.le.trans","Lattice.toSemilatticeInf","LipschitzWith","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm","Norm.norm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedRing.toNorm","OfNat.ofNat","PartialOrder.toPreorder","Pi.complete","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedRing","Pi.normedSpace","Pi.seminormedAddGroup","Pi.topologicalSpace","Preorder.toLE","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.EqOn","Set.Icc","Set.instMembership","Set.uIcc","Set.uIcc_of_le","Subtype.property","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreHamiltonianJointStability.0.GinibrePoincare.ginibreDrivenSegment_joint_stability_in_extension._abel_1_1","_private.GinibrePoincare.Analysis.GinibreHamiltonianJointStability.0.GinibrePoincare.ginibreDrivenSegment_joint_stability_in_extension._abel_1_2","congrArg","id","instHAdd","instHSub","instInnerProductSpaceRealComplex","instTransEq","instTransLE","intervalIntegral","intervalIntegral.integral_congr","norm_add_le","pseudoEMetricSpacePi"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianJointTube","name":"GinibrePoincare.ginibreDrivenSegment_joint_stays_tube","type_dependencies":["CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","Complex","Complex.instNormedField","Complex.instSub","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","LipschitzWith","Membership.mem","Metric.cthickening","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","Norm.norm","NormedField.toMetricSpace","NormedRing.toNorm","OfNat.ofNat","Pi.instSub","Pi.normedRing","Real","Real.exp","Real.instAdd","Real.instLE","Real.instLT","Real.instMul","Real.instPreorder","Real.instZero","Set","Set.EqOn","Set.Icc","Set.instMembership","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHMul","instHSub","pseudoEMetricSpacePi"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.intro","And.left","And.right","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Comple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instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","DFunLike.coe","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Finset.sum","Finset.univ","Finsupp","Finsupp.instAdd","Finsupp.instAddCommMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.ginibreEquality_symmetric_homogeneous_one","GinibrePoincare.isSymmetric_quotient_of_vandermonde_mul_alternating","GinibrePoincare.polynomialVandermonde","HAdd.hAdd","HMul.hMul","HPow.hPow","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.IsHomogeneous","MvPolynomial.X","NPow.toPow","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","RingHom","RingHom.instFunLike","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityFullGenerator","name":"GinibrePoincare.ginibreEquality_centered_inner","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreL2Mean","GinibrePoincare.ginibreMeasure","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincar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andermondeDegree","GinibrePoincare.vandermonde_ne_zero_iff","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasDistribNeg.toInvolutiveNeg","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","InvolutiveNeg.toNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MvPolynomial","MvPolynomial.IsHomogeneous","MvPolynomial.IsHomogeneous.totalDegree","MvPolynomial.eval","MvPolynomial.totalDegree","MvPolynomial.totalDegree_mul_of_isDomain","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.decLe","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormMulClass.toNoZeroDivisors","NormOneClass.norm_one","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","One.toOfNat1","Or","Or.resolve_left","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instFloorRing","Real.instNatCast","Real.instOne","Real.instRing","Real.linearOrder","Real.partialOrder","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","True.intro","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreEqualityFirstQuotient.0.GinibrePoincare.ginibreEquality_finite_first_quotient_ae_coordinateSum._proof_1_1","cast","congr","congrArg","congrFun'","eq_self","eq_true","funext","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_eq_zero","mul_neg","neg_mul","neg_one_mul","norm_neg","of_eq_true","one_mul","pow_one","rfl","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityFiniteConjugateDegree","name":"GinibrePoincare.ginibreEquality_finite_quotient_conjugate_degree_bound","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","Finset","Finset.instSetLike","Finsupp","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.IsFiniteHomogeneousQuotientVector","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","CStarRing.to_normedStarGroup","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","Decidable.byContradiction","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.ndrec","Eq.symm","Exists","Exists.casesOn","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsFiniteHomogeneousQuotientVector","GinibrePoincare.IsFiniteHomogeneousQuotientVector._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteHomogeneousQuotientL2","GinibrePoincare.finiteHomogeneousQuotientL2_coeFn","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreCons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roup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","CStarRing.to_normedStarGroup","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.symm","Exists","Exists.casesOn","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsFiniteHomogeneousQuotientVector","GinibrePoincare.IsFiniteHomogeneousQuotientVector._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.finiteHomogeneousQuotientL2","GinibrePoincare.finiteHomogeneousQuotientL2_mem_phaseDegree","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreEquality_finite_quotient_conjugate_degree_bound","GinibrePoincare.ginibreEquality_phase_conjugate_low_modes_finite","GinibrePoincare.ginibreGlobalPhaseL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.globalPhase","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.polynomialVandermonde","GinibrePoincare.totalHolomorphicDegree","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSub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Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityMixedFactor","name":"GinibrePoincare.ginibreEquality_mixed_factor_degree_bound_of_specialize","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AlgHom","AlgHom.funLike","Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instZero","DFunLike.coe","Eq","Fin","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedAntiholomorphicLift","GinibrePoincare.ginibreMixedHolomorphicLift","GinibrePoincare.ginibreMixedPolynomialSpecialize","HMul.hMul","LE.le","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","MvPolynomial.totalDegree","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","OfNat.ofNat","Prod","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0","instHMul","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.instDecidableEq","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","AlgHom","AlgHom.algHomClass","AlgHom.funLike","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","Algebra.id","Algebra.toModule","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instDecidableEq","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.instZero","DFunLike.coe","Eq","Eq.mp","Eq.mpr","Eq.trans","Fin","Finset","Finset.sup","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.instDecidableEq","Finsupp.sum","Function.Injective","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.GinibreMixedPolynomial","GinibrePoincare.ginibreMixedAntiholomorphicLift","GinibrePoincare.ginibreMixedHolomorphicLift","GinibrePoincare.ginibreMixedPolynomialSpecialize","GinibrePoincare.ginibreMixedPolynomialSpecialize_antiholomorphic","GinibrePoincare.ginibreMixedPolynomialSpecialize_holomorphic","HAdd.hAdd","HMul.hMul","Iff.mpr","LE.le","Lattice.toSemilatticeSup","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidHom.id","MonoidWithZeroHomClass.toZeroHomClass","MulOneClass.toMulOne","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.C_ne_zero","MvPolynomial.eval","MvPolynomial.map","MvPolynomial.map_injective","MvPolynomial.support","MvPolynomial.support_map_of_injective","MvPolynomial.totalDegree","MvPolynomial.totalDegree_C","MvPolynomial.totalDegree_mul_of_isDomain","MvPolynomial.totalDegree_zero","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instLattice","Nat.instLinearOrderedCommMonoidWithZero","Nat.instMulZeroClass","Nat.instOrderBot","Ne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalAlgSemiHomClass.toMulHomClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","Prod","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","True","Zero.toOfNat0","congrArg","congrFun'","dite","eq_self","id","instAddNat","instDecidableEqFin","instDecidableEqNat","instHAdd","instHMul","instLENat","instMulZeroClassOfSemiring","instOfNatNat","map_mul","map_zero","of_eq_true","starRingEnd","star_injective","zero_add","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityCore","name":"GinibrePoincare.ginibreEquality_modeTail_eq_zero_iff","type_dependencies":["Eq","GinibrePoincare.modeTail","HMul.hMul","Iff","LE.le","LT.lt","Nat","Nat.cast","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instZero","Real.pseudoMetricSpace","Summable","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CharP.cast_eq_zero","CharP.ofCharZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","FloorRing.toFloorSemiring"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":"GinibrePoincare.ginibreEquality_positive_conjugate_low_modes_mem_first","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","ClosedSubmodule","ClosedSubmodule.instSetLike","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","GinibrePoincare.normalizedVandermondeL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.true","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","ClosedSubmodule","ClosedSubmodule.instCompleteLatticeOfT1Space","ClosedSubmodule.instPartialOrder","ClosedSubmodule.instSetLike","ClosedSubmodule.mem_toSubmodule_iff._simp_1","ClosedSubmodule.mk","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.isClosed_ker","ContinuousLinearMap.module","ContinuousLinearMap.toLinearMap","ContinuousLinearMap.topologicalSpace","DFunLike.coe","Decidable.byContradiction","Decidable.decide","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreEquality_high_quotient_projection_zero","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan.congr_simp","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan_le_positive","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan_orthogonal","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","GinibrePoincare.normalizedVandermondeL2","HSub.hSub","Iff.mp","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearIsometry","LinearIsometry.instFunLike","LinearMap.ker","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.decLe","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne.symm","NegZeroClass.toZero","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.IsOrtho.inner_eq","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Submodule.starProjection_apply_mem","Submodule.starProjection_inner_eq_zero","Submodule.sub_mem","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","T5Space.toT1Space","T6Space.toT5Space","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreEqualityWeakDegreeElimination.0.GinibrePoincare.ginibreEquality_positive_conjugate_low_modes_mem_first._proof_1_1","congrArg","congrFun'","dite","fact_one_le_two_ennreal","iSup_le","id","innerSL","inner_self_eq_zero","inner_sub_left","instCommCStarAlgebraComplex","instDecidableEqNat","instDistribOfSemiring","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instT6SpaceOfMetrizableSpace","of_decide_eq_true","starRingEnd","sub_eq_zero","sub_self","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityPolynomial","name":"GinibrePoincare.ginibreEquality_symmetric_affine","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instMul","AddMo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rFun'","eq_self","id","instHMul","instLTNat","instOfNatNat","map_mul","map_sum","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityPolynomial","name":"GinibrePoincare.ginibreEquality_symmetric_linear_coeff","type_dependencies":["AddMonoidAlgebra.coeff","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","DFunLike.coe","Eq","Fin","Finsupp","Finsupp.instFunLike","Finsupp.single","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","OfNat.ofNat","instMulZeroClassOfSemiring","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.coeff","AddMonoidAlgebra.semiring","AddZero.toZero","AddZeroClass.toAddZero","AlgHom","AlgHom.funLike","Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","DFunLike.coe","Eq","Eq.mp","Equiv.injective","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_left","EquivLike.toFunLike","Fin","Finsupp","Finsupp.instAddMonoid","Finsupp.instFunLike","Finsupp.mapDomain","Finsupp.mapDomain_single","Finsupp.single","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.permuteConfigurationPolynomial","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff_rename_mapDomain","MvPolynomial.rename","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","congrArg","congrFun'","id","instDecidableEqFin","instMulZeroClassOfSemiring","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakConjugateModes","name":"GinibrePoincare.ginibreEquality_weak_conjugate_higher_modes_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.normalizedVandermondeL2","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMul","Real.instNatCast","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLik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ullHigherMode._proof_2","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.tsum_gaussianHermiteMode","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Insert.insert","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MulZeroClass.toZero","Nat","Nat.decLe","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instOne","Nat.sub_add_cancel","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","Or","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMul","Real.instNatCast","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Singleton.singleton","Subtype","SummationFilter.instLeAtTopUnconditional","SummationFilter.unconditional","Trans.trans","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreEqualityWeakModes.0.GinibrePoincare.ginibreEquality_weak_transform_low_modes._proof_1_1","_private.GinibrePoincare.Analysis.GinibreEqualityWeakModes.0.GinibrePoincare.ginibreEquality_weak_transform_low_modes._proof_1_2","_private.GinibrePoincare.Analysis.GinibreEqualityWeakModes.0.GinibrePoincare.ginibreEquality_weak_transform_low_modes._proof_1_3","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instAddNat","instCommCStarAlgebraComplex","instDecidableEqNat","instFintypeProd","instHAdd","instHMul","instHSub","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat","instTransEq","not_false_eq_true","of_eq_true","one_ne_zero._simp_1","or_false","or_true","tsum","tsum_eq_sum","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreEquality_weak_variational_iff","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","HDiv.hDiv","HMul.hMul","Iff","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.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inormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianEquilibriumProductLaw","name":"GinibrePoincare.ginibreEquilibriumProduct_pathMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEquilibriumProcessStationarityPath","name":"GinibrePoincare.ginibreEquilibriumShiftedPositivePath","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","NNReal","NNReal.instTopologicalSpace","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap.comp","ContinuousMap.mk","Distrib.toAdd","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreEquilibriumPositivePath","GinibrePoincare.ginibreEquilibriumShiftedPositivePath._proof_1","HAdd.hAdd","NNReal","NNReal.instSemiring","NNReal.instTopologicalSpace","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEquilibriumProcessStationarityPath","name":"GinibrePoincare.ginibreEquilibriumShiftedPositivePath._proof_1","type_dependencies":["Continuous","Distrib.toAdd","HAdd.hAdd","NNReal","NNReal.instSemiring","NNReal.instTopologicalSpace","Pi.instAdd","instDistribOfSemiring","instHAdd"],"value_dependencies":["Continuous.add","Distrib.toAdd","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalSemiring.toIsSemitopologicalSemiring","NNReal","NNReal.instIsTopologicalSemiring","NNReal.instSemiring","NNReal.instTopologicalSpace","NonAssocSemiring.toNonUnitalNonAssocSemiring","Semiring.toNonAssocSemiring","continuous_const","continuous_id","instDistribOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEquilibriumProcessStationarityPath","name":"GinibrePoincare.ginibreEquilibriumShiftedPositivePath.eq_1","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.comp","ContinuousMap.mk","Distrib.toAdd","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreEquilibriumPositivePath","GinibrePoincare.ginibreEquilibriumShiftedPositivePath","GinibrePoincare.ginibreEquilibriumShiftedPositivePath._proof_1","HAdd.hAdd","NNReal","NNReal.instSemiring","NNReal.instTopologicalSpace","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreEquilibriumShiftedPositivePath","NNReal","NNReal.instTopologicalSpace","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","i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Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.norm","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithLp.ofLp","WithTop.some","Zero.toOfNat0","congrArg","congrFun'","fderiv","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instTopENat","le_of_not_gt","rfl","sq_abs","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakGradient","name":"GinibrePoincare.ginibreEuclideanGradient_coordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreEuclideanGradient","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.ofLp","fderiv","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreCoordinateDirection._proof_1","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient._proof_2","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.ofLp","congr","congrArg","dite","fderiv","id","instDecidableEqFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_left","ite_eq_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSmoothSobolevApproximation","n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g.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","T5Space.toT1Space","T6Space.toT5Space","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instT6SpaceOfMetrizableSpace","le_iSup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan_orthogonal","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule.IsOrtho","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan_le_phaseDegree","GinibrePoincare.ginibreHolomorphicPhaseDegree","GinibrePoincare.ginibreHolomorphicPhaseDegree_orthogonal","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat",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","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan._proof_1","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan._proof_2","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","iSup","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","name":"GinibrePoincare.ginibreFiniteVectorNoiseLift","type_dependencies":["Fin","GinibrePoincare.Configuration","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Prod","Real","Real.instPreorder","Real.instZero","Set.Elem","Set.Icc","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianEmbeddingCLM","GinibrePoincare.ginibreFiniteVectorNoiseLift._proof_1","InnerProductSpace.toNormedSpace","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","name":"GinibrePoincare.ginibreFiniteVectorNoiseLift._proof_1","type_dependencies":["And","LE.le","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instPreorder","Real.instZero","Real.toNNReal","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","Zero.toOfNat0"],"value_dependencies":["And.intro","And.right","Iff.mpr","LE.le","Membership.mem","NNReal","NNReal.instOrderBot","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.toNNReal","Real.toNNReal_le_iff_le_coe","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","Subtype.val","Zero.toOfNat0","bot_le"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","name":"GinibrePoincare.ginibreFiniteVectorNoiseLift_configurationNoise","type_dependencies":["Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreFiniteVectorNoiseLift","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Prod","Real","Real.instPreorder","Real.instZero","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteVectorNoiseLift","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Prod","Real","Real.instPreorder","Real.instZero","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.val","Zero.toOfNat0","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","name":"GinibrePoincare.ginibreFiniteVectorNoiseLift_law","type_dependencies":["And","Complex","Complex.measurableSpace","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteVectorNoiseLift","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Prod","Real","Real.instPreorder","Real.instZero","Real.measurableSpace","Set.Elem","Set.Icc","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["And","And.intro","Complex","Complex.measurableSpace","Eq","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteVectorNoiseLift","GinibrePoincare.ginibreFiniteVectorNoiseLift_measurable","Measurable","Measurable.aemeasurable","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","ProbabilityTheory.IdentDistrib","ProbabilityTheory.IdentDistrib.comp","ProbabilityTheory.IdentDistrib.map_eq","ProbabilityTheory.IdentDistrib.mk","Prod","Real","Real.instPreorder","Real.instZero","Real.measurableSpace","Set.Elem","Set.Icc","Zero.toOfNat0","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","name":"GinibrePoincare.ginibreFiniteVectorNoiseLift_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteVectorNoiseLift","Measurable","MeasurableSpace.pi","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","OfNat.ofNat","PartialOrder.toPreorder","Prod","Real","Real.instPreorder","Real.instZero","Real.measurableSpace","Set.Elem","Set.Icc","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.measurable","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianEmbeddingCLM","GinibrePoincare.ginibreFiniteVectorNoiseLift","GinibrePoincare.ginibreFiniteVectorNoiseLift._proof_1","InnerProductSpace.toNormedSpace","Measurable.comp","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.borelSpace","Pi.opensMeasurableSpace","Pi.seminormedAddCommGroup","PolishSpace.toSecondCountableTopology","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instFintypeProd","instInnerProductSpaceRealComplex","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurable_pi_apply","measurable_pi_lambda","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalFreeInitial","name":"GinibrePoincare.ginibreFreeInitialVersion","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","Nat","Subtype"],"value_dependencies":["Classical.propDecidable","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","Nat","Not","Subtype","Subtype.mk","dite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalEquilibriumFactorization","name":"GinibrePoincare.ginibreFreeInitialVersion.congr_simp","type_dependencies":["Eq","Eq.ndrec","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","Nat","Subtype"],"value_dependencies":["Eq","Eq.ndrec","Eq.rec","Eq.refl","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","Nat","Subtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalFreeInitial","name":"GinibrePoincare.ginibreFreeInitialVersion.eq_1","type_dependencies":["Classical.propDecidable","Eq","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","Nat","Not","Subtype","Subtype.mk","dite"],"value_dependencies":["Eq.refl","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","Nat","Subtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalFreeInitial","name":"GinibrePoincare.ginibreFreeInitialVersion_ae_eq","type_dependencies":["Complex","Complex.measurableSpace","Filter.EventuallyEq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Nat","OfNat.ofNat","Subtype.val","id","instLTNat","instOfNatNat"],"value_dependencies":["Classical.propDecidable","Complex","Complex.measurableSpace","Eq","Eq.trans","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_ae_collisionFree","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.mk","Subtype.val","True","congrArg","congrFun'","dite_eq_left_of_eq_true","eq_self","eq_true","id","instLTNat","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalFreeInitial","name":"GinibrePoincare.ginibreFreeInitialVersion_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreFreeInitialVersion","Measurable","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace"],"value_dependencies":["Bool","Bool.Reflects","Bool.rec","BorelSpace.opensMeasurable","Classical.propDecidable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Decidable.decide","Decidable.reflects_decide","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.isOpen_collisionFree","HEq","HEq.refl","IsOpen.measurableSet","Measurable","Measurable.ite","Measurable.subtype_mk","MeasurableSpace","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Not","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.ofPred","Subtype","Subtype.mk","Subtype.property","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","congrArg","dif_neg","dif_pos","dite","eq_of_heq","funext","id","if_neg","if_pos","instCommCStarAlgebraComplex","instCountableFin","ite","measurable_const","measurable_id","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullBackwardEuler_nonneg","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.Eventually","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.resolventBackwardEuler","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instLT","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","And.intro","And.left","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.map_smul","ContinuousLinearMap.map_sub","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.Eventually","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_isSelfAdjoint","GinibrePoincare.ginibreFullComplexResolvent_spectrum","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullGenerator_backward_nonneg","GinibrePoincare.ginibreFullGenerator_graph_iff","GinibrePoincare.ginibreFullGenerator_graph_iff_real_imag","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricIm_ofReal","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricRe_ofReal","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSy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inibrePoincare.resolventBackwardEuler","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instLT","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.innerProductSpace","Submodule.isTopologicalAddGroup","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsOneApply","ContinuousLinearMap.semiring","ContinuousLinearMap.toLinearMap","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Filter","Filter.Eventually","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullBackwardEuler_nonneg","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.resolventBackwardEuler","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.recAux","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instLT","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.innerProductSpace","Submodule.isTopologicalAddGroup","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instAddNat","instCommCStarAlgebraComplex","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","one_apply_eq_self","pow_succ'","pow_zero"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.module","ContinuousLinearMap.smulRight","ContinuousLinearMap.sub","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreFullCenter._proof_10","GinibrePoincare.ginibreFullCenter._proof_11","GinibrePoincare.ginibreFullCenter._proof_12","GinibrePoincare.ginibreFullCenter._proof_13","GinibrePoincare.ginibreFullCenter._proof_2","GinibrePoincare.ginibreFullCenter._proof_3","GinibrePoincare.ginibreFullCenter._proof_4","GinibrePoincare.ginibreFullCenter._proof_5","GinibrePoincare.ginibreFullCenter._proof_8","GinibrePoincare.ginibreFullCenter._proof_9","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.instAddCommMonoid","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","innerSL","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_10","type_dependencies":["AddCommGroup.toAddGroup","DenselyNormedField.toNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_11","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","DenselyNormedField.toNormedField","Distrib.toAdd","Field.toCommRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","DenselyNormedField.toNormedField","Field.toCommRing","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_12","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","SMulCommClass","Semifield.toCommSemiring","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_13","type_dependencies":["CommSemiring.toSemiring","ContinuousConstSMul","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instDistribOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_3","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreFullCenter._proof_2","GinibrePoincare.ginibreMeasure","IsTopologicalAddGroup","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","ContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup.toContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.measurableSpace","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreFullCenter._proof_2","GinibrePoincare.ginibreFullCenter._proof_6","GinibrePoincare.ginibreFullCenter._proof_7","GinibrePoincare.ginibreMeasure","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommSemiring.toSemiring","Complex","Complex.measurableSpace","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.Lp.instIsScalarTower","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","OfNat.ofNat","RCLike.toDenselyNormedField","Real","Real.instCommSemiring","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreFullCenter._proof_2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toS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","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakVariational","name":"GinibrePoincare.ginibreFullCenter_apply","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreL2Mean","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.module","ContinuousLinearMap.smulRight","ContinuousLinearMap.sub","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullCenter._proof_1","GinibrePoincare.ginibreFullCenter._proof_10","GinibrePoincare.ginibreFullCenter._proof_11","GinibrePoincare.ginibreFullCenter._proof_12","GinibrePoincare.ginibreFullCenter._proof_13","GinibrePoincare.ginibreFullCenter._proof_2","GinibrePoincare.ginibreFullCenter._proof_3","GinibrePoincare.ginibreFullCenter._proof_4","GinibrePoincare.ginibreFullCenter._proof_5","GinibrePoincare.ginibreFullCenter._proof_8","GinibrePoincare.ginibreFullCenter._proof_9","GinibrePoincare.ginibreL2Mean","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","GinibrePoincare.ginibreRealConstantL2._proof_1","GinibrePoincare.ginibreRealConstantL2_ae","HMul.hMul","HSMul.hSMul","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNa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orm._proof_1","GinibrePoincare.ginibreFullCenteredTransform._proof_10","GinibrePoincare.ginibreFullCenteredTransform._proof_2","GinibrePoincare.ginibreFullCenteredTransform._proof_3","GinibrePoincare.ginibreFullCenteredTransform._proof_4","GinibrePoincare.ginibreFullCenteredTransform._proof_5","GinibrePoincare.ginibreFullCenteredTransform._proof_6","GinibrePoincare.ginibreFullCenteredTransform._proof_7","GinibrePoincare.ginibreFullCenteredTransform._proof_9","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_10","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_3","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_5","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullCenteredTransform._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullCenteredTransform._proof_7","type_dependencies":["Complex","Complex.instNonUnitalCommRing"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ibreRealConstantL2._proof_1","GinibrePoincare.ginibreRealConstantL2_ae","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.smoothGinibreMean","GinibrePoincare.transformedCenteredObservableL2","GinibrePoincare.transformedCenteredObservableL2._proof_1","GinibrePoincare.transformedCenteredObservableL2._proof_2","HEq","HEq.refl","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_sub","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral_congr_ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instSub","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","eq_of_heq","fact_one_le_two_ennreal","heq_of_eq","id","instCommCStarAlgebraComplex","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakDeficit","name":"GinibrePoincare.ginibreFullCenteredValue_core","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.centeredObservableL2","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNor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iring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule.smulMemClass","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDecay","name":"GinibrePoincare.ginibreFullComplexCenter._proof_11","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousSMul","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter._proof_1","GinibrePoincare.ginibreFullComplexCenter._proof_10","GinibrePoincare.ginibreFullComplexCenter._proof_2","GinibrePoincare.ginibreFullComplexCenter._proof_3","GinibrePoincare.ginibreFullComplexCenter._proof_5","GinibrePoincare.ginibreFullComplexCenter._proof_6","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SetLike.smul","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex"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mplex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDecay","name":"GinibrePoincare.ginibreFullComplexCenter._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter._proof_1","GinibrePoincare.ginibreFullComplexCenter._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDecay","name":"GinibrePoincare.ginibreFullComplexCenter._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDecay","name":"GinibrePoincare.ginibreFullComplexCenter._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter._proof_1","GinibrePoincare.ginibreFullComplexCenter._proof_2","GinibrePoincare.ginibreFullComplexCenter._proof_6","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","IsTopologicalAddGroup","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAd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omplex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter","GinibrePoincare.ginibreFullComplexCenter_apply","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullConstant_eq_smul_one","GinibrePoincare.ginibreFullConstant_norm_one","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCom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dGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.imCLM","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousLinearMap.compLpL","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreFullComplexRe._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.semiring","RingHom.id","Semiring.toNonAssocSemiring","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexIm_I","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreMeasure","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","Co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ormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofRealCLM","ContinuousLinearMap.coeFn_compLpL","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","RingHom.id","RingHomIsometric.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexRe","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.reCLM","ContinuousLinearMap.compLpL","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreFullComplexRe._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.semiring","RingHom.id","Semiring.toNonAssocSemiring","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexRe._proof_1","type_dependencies":["NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","Ring.toSemiring","RingHom.id","RingHomIsometric","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toNonAssocSemiring"],"value_dependencies":["NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","RingHomIsometric.ids","SeminormedCommRing.toSeminormedRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexRe_I","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreMeasure","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.mul_re","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexIm_ae","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ae","GinibrePoincare.ginibreMeasure","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_neg","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Neg.neg","NegZeroClass.toNeg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instNeg","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instMul","Real.instNeg","Real.instRCLike","Real.instSub","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemi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SpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreFullComplexResolventReal","GinibrePoincare.ginibreFullSymmetricRe._proof_10","GinibrePoincare.ginibreFullSymmetricRe._proof_2","GinibrePoincare.ginibreFullSymmetricRe._proof_3","GinibrePoincare.ginibreFullSymmetricRe._proof_5","GinibrePoincare.ginibreFullSymmetricRe._proof_6","GinibrePoincare.ginibreFullSymmetricRe._proof_8","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap.continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolventReal","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionR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HSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolventReal","GinibrePoincare.ginibreFullComplexResolventReal_I","GinibrePoincare.ginibreFullComplex_scalar_decomposition","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.toAddHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.add","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","map_add","map_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolventLinear._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.i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ring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.zero","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_im","GinibrePoincare.ginibreFullComplexResolvent_re","GinibrePoincare.ginibreFullComplex_decomposition","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricResolvent_eq_zero_iff","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HSMul.hSMul","Iff.intro","Iff.mp","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","Se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e.ginibreFullSymmetricRe._proof_3","GinibrePoincare.ginibreFullSymmetricRe._proof_5","GinibrePoincare.ginibreFullSymmetricRe._proof_6","GinibrePoincare.ginibreFullSymmetricRe._proof_7","GinibrePoincare.ginibreFullSymmetricRe._proof_8","GinibrePoincare.ginibreFullSymmetricRe_ofReal","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.toAddHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.add","Submodule.addCommMonoid","Submodule.addSubmonoidClass","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Submodule.zero","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","map_add","of_eq_true","smul_apply","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_injective","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Function.Injective","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_eq_zero_iff","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.setLike","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","map_sub","sub_eq_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_inner_nonneg","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass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e","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HMul.hMul","HPow.hPow","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toIsOrderedRing","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Lattice.toSemilatticeInf","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Preorder.toLE","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.module'","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdNormedAddCommGroup","Zero.toOfNat0","add_nonneg","congrArg","even_two_mul","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_isPositive","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap.IsPositive","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAdd","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.mk","AddZeroClass.toAddZero","And.intro","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.reApplyInnerSelf","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_inner_nonneg","GinibrePoincare.ginibreFullComplexResolvent_symmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap.IsSymmetric","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.re","RCLike.toDenselyNormedField","Real","Real.instAddMonoid","Real.instLE","Real.instZero","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","inner_re_symm","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_isSelfAdjoint","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.instStarId","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSelfAdjoint","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.instStarId","ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric","ContinuousLinearMap.toLinearMap","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_symmetric","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","Iff.mpr","InnerProductSpace.toNormedSpace","IsSelfAdjoint","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap.IsSymmetric","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_norm_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instLE","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Bool","Bool.false","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearM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NonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","fact_one_le_two_ennreal","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopologicalSpaceSubtype","le_of_lt","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","mul_pos_of_neg_of_neg","neg_eq_zero","norm_nonneg","rfl","sq_le_sq\u2080","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorCoreIdentification","name":"GinibrePoincare.ginibreFullComplexResolvent_ofReal","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","M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ullSymmetricRe._proof_6","GinibrePoincare.ginibreFullSymmetricRe._proof_7","GinibrePoincare.ginibreFullSymmetricRe._proof_8","GinibrePoincare.ginibreFullSymmetricRe_ofReal","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.add","Submodule.addCommMonoid","Submodule.addSubmonoidClass","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Submodule.zero","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","add_zero","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","map_zero","of_eq_true","smul_apply","smul_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_opNorm_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace"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seudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_re","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMono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","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.add","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.addSubmonoidClass","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","add_zero","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","map_add","neg_zero","of_eq_true","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplexResolvent_spectrum","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.ring","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.isScalarTower'","Submodule.isTopologicalAddGroup","Submodule.module","Submodule.module'","Submodule.module._proof_1","Submodule.normedSpace","Submodule.se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edRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplex_decomposition","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.I","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMono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orm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.integrable_mul","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_add","MeasureTheory.integral_congr_ae","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.lattice","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","TopologicalSpace","True","UniformSpace.toTopologicalSpace","abs","abs_mul_abs_self","autoParam","congr","congrArg","congrFun'","eq_of_heq","eq_self","fact_one_le_two_ennreal","funext","id","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","pow_two","sq_abs"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullComplex_scalar_decomposition","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.re","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.add","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","Complex.re","Complex.re_add_im","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","Membership.mem","Module.complexToReal","Module.toDistribMulAction","MulAction.toSemigroupAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.toMul","SemigroupAction.mul_smul","SemigroupAction.toSMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.add","Submodule.setLike","Submodule.smul","Subtype","Subtype.ext","Subtype.val","UniformSpace.toTopologicalSpace","add_smul","congrArg","eq_self","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"GinibrePoincare.ginibreFullConjugateAntiMode","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap.comp","ContinuousLinearMap.restrictScalars","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullConjugateAntiMode._proof_1","GinibrePoincare.ginibreFullConjugateAntiMode._proof_10","GinibrePoincare.ginibreFullConjugateAntiMode._proof_11","GinibrePoincare.ginibreFullConjugateAntiMode._proof_12","GinibrePoincare.ginibreFullConjugateAntiMode._proof_2","GinibrePoincare.ginibreFullConjugateAntiMode._proof_3","GinibrePoincare.ginibreFullConjugateAntiMode._proof_5","GinibrePoincare.ginibreFullConjugateAntiMode._proof_7","GinibrePoincare.ginibreFullConjugateAntiMode._proof_8","GinibrePoincare.ginibreFullConjugateAntiMode._proof_9","GinibrePoincare.ginibreFullLpConjugationIsometry","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry.toContinuousLinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"GinibrePoincare.ginibreFullConjugateAntiMode._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"GinibrePoincare.ginibreFullConjugateAntiMode._proof_10","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"GinibrePoincare.ginibreFullConjugateAntiMode._proof_11","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullConjugateAntiMode._proof_1","GinibrePoincare.ginibreFullConjugateAntiMode._proof_10","GinibrePoincare.ginibreFullConjugateAntiMode._proof_2","GinibrePoincare.ginibreFullConjugateAntiMode._proof_3","GinibrePoincare.ginibreFullConjugateAntiMode._proof_7","GinibrePoincare.ginibreFullConjugateAntiMode._proof_8","InnerProductSpace.toNormedSpace","LinearMap.CompatibleSMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSp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"type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupConservation","name":"GinibrePoincare.ginibreFullConstant._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullConstant._proof_2","GinibrePoincare.ginibreFullConstant._proof_5","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupConservation","name":"GinibrePoincare.ginibreFullConstant._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupConservation","name":"GinibrePoincare.ginibreFullConstant.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.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"LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.exp","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Continuous.clm_apply","Continuous.comp'","Continuous.const_mul","Continuous.fun_pow","Continuous.norm","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousLinearMap.topologicalSpace","DFunLike.coe","Dense.closure_eq","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexCenter","GinibrePoincare.ginibreFullComplexCenter_graph","GinibrePoincare.ginibreFullComplexCenter_mean_zero","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullEvolution_decay_sq_on_domain","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullGenerator_dense_domain","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","HPow.hPow","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsClosed","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LinearPMap.domain","LinearPMap.graph","LinearPMap.mem_graph","LinearPMap.toFun'","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCStarAlgebra.toIsScalarTower","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedC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GroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_spectrum","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.resolventCfcEvolution_contracts","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorCenterEigenvectors","name":"GinibrePoincare.ginibreFullEvolution_coordinateSum","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat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edAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.Ioi","Set.instMembership","Set.mem_Ici._simp_1","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.module'","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","antitoneOn_of_hasDerivWithinAt_nonpos","congr","congrArg","congrFun'","continuous_id'","continuous_mul","continuous_real_toNNReal","convex_Ici","eq_of_heq","eq_self","fact_one_le_two_ennreal","funext","hasDerivAt_id","id","inferInstance","inner_re_symm","instAddNat","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsOrderedModule","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instNoMinOrderOfNontrivial","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instPolynormableSpace","instReflLe","instStarRingReal","instTopologicalSpaceProd","instTopologicalSpaceSubtype","interior","interior_Ici","le_of_not_gt","mul_assoc","mul_comm","mul_le_mul_of_nonneg_left","mul_nonpos_of_nonneg_of_nonpos","of_eq_true","one_apply_eq_self","one_mul","real_inner_eq_re_inner","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDynamics","name":"GinibrePoincare.ginibreFullEvolution_eigenvector","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Normed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inibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_spectrum","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.resolventCfcEvolution_norm_le","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullEvolution_ofReal","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpa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erProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.zero","Subtype","Subtype.ext","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","map_zero","smul_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialCompatibility","name":"GinibrePoincare.ginibreFullEvolution_polynomialSector","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullEvolution_polynomial_eigenvector._proof_2","GinibrePoincare.ginibreFullPolynomialSectorInclusion","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.polynomialSectorEvolution","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.algebraMap","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","Decidable.byContradiction","DenseRange.induction_on","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instFunLike","Finsupp.linearCombination","Finsupp.linearCombination_apply","Finsupp.module","Finsupp.sum","Finsupp.sum.eq_1","Finsupp.support","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullEvolution_polynomial_eigenvector","GinibrePoincare.ginibreFullEvolution_polynomial_eigenvector._proof_2","GinibrePoincare.ginibreFullPolynomialEigenvector","GinibrePoincare.ginibreFullPolynomialSectorInclusion","GinibrePoincare.ginibreFullPolynomialSectorInclusion_eigenvector","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.polynomialSectorCombination","GinibrePoincare.polynomialSectorCombination_dense","GinibrePoincare.polynomialSectorEigenvector","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorEvolution","GinibrePoincare.polynomialSectorEvolution_eigenvector","HMul.hMul","HSMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.toZero","NNReal","NNReal.toReal","Nat","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.exp","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.in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ormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDecay","name":"GinibrePoincare.ginibreFullEvolution_tendsto_equilibrium","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.integral","Membership.mem","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instRCLike","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.const_mul_atTop","Filter.Tendsto.mul_const","Filter.atTop","Filter.tendsto_id","Fin","FloorRing.toFloorSemiring","Floor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roup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.addCommGroup","Pi.instSMul","PiLp","PiLp.innerProductSpace._proof_1","PiLp.instPseudoMetricSpace","Prod","Real","Real.normedCommRing","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","WithLp.instAddCommGroup","WithLp.instSMul","fact_one_le_two_ennreal","instFintypeProd","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","Prod","Real","Real.isBoundedSMul","Real.normedCommRing","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormCoordinates._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup.toContinuousAdd","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","Real.normedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormCoordinates._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSemin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inibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullFormOfWeak","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreFullFormValue","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAd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toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instRCLike","RingHomInvPair.instStarRingEnd","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_2","type_dependencies":["DenselyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","Ring.toSemiring","RingHom.id","RingHomIsometric","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toNonAssocSemiring"],"value_dependencies":["DenselyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHomIsometric.ids","SeminormedCommRing.toSeminormedRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_3","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","SMulCommClass","Semifield.toCommSemiring","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_4","type_dependencies":["CommSemiring.toSemiring","ContinuousConstSMul","DenselyNormedField.toNormedField","Distrib.toMul","Field.toSemifield","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instDistribOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","ContinuousAdd","DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["ContinuousLinearMap.addCommGroup._proof_7","DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_6","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_7","type_dependencies":["AddCommGroup.toAddGroup","DenselyNormedField.toNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["DenselyNormedField.toNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolvent._proof_8","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","DenselyNormedField.toNormedField","Distrib.toAdd","Field.toCommRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","DenselyNormedField.toNormedField","Field.toCommRing","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormResolventCLM","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGro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oof_4","GinibrePoincare.ginibreFullFormCoordinates._proof_5","GinibrePoincare.ginibreFullFormSpace._proof_1","GinibrePoincare.ginibreFullFormSpace._proof_2","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.comap","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormSpace._proof_1","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormSpace._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullFormSpace_complete","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","CompleteSpace","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbien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","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Preorder.toLT","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","inferInstance","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","instTopologicalSpaceSubtype","neg_eq_zero","rfl","secondCountableTopologyEither_of_right","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorCenterEigenvectors","name":"GinibrePoincare.ginibreFullGenerator_centerOfMassReal_eigenvector","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","Gi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","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.module'","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","And","And.casesOn","Bool","Bool.false","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","EuclideanSpace","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullGenerator_complex_energy_identity","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.ginibre_symmetric_weak_poincare","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearOrder.toPartialOrder","LinearPMap.graph","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.No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nibrePoincare.ginibreFullGenerator_constant","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.module","Submodule.setLike","Submodule.zero","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_constant","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullGenerator_graph_iff","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.setLike","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","propext","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorCenterEigenvectors","name":"GinibrePoincare.ginibreFullGenerator_coordinateSum_eigenvector","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","And","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Field.toDivisionRing","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.module","Submodule.setLike","Submodule.smul","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidW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Poincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.complexGinibrePregenerator","GinibrePoincare.complexGinibrePregenerator_coordinateSum_power","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCoordinateSumPowerL2","GinibrePoincare.ginibreCoordinateSumPowerL2_ae","GinibrePoincare.ginibreFullComplexIm","GinibrePoincare.ginibreFullComplexIm_ae","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ae","GinibrePoincare.ginibreFullComplex_decomposition","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibreSymmetricL2","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Prod","Prod.ext","Prod.instAdd","Prod.instAddCommMonoid","Prod.instModule","Prod.instSMul","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","SMulCommClass.smul_comm","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.add","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubmonoidClass","Submodule.add_mem","Submodule.isScalarTower'","Submodule.module","Submodule.module'","Submodule.module._proof_1","Submodule.setLike","Submodule.smul","Submodule.smul_mem","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.ext","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreOneParticleSpectrum.0.GinibrePoincare.coordinateSum_power_projected_graph","add_zero","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","forall_congr","id","instCommCStarAlgebraComplex","instDistribO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ofNat","instLENat","instLTNat","instOfNatNat"],"value_dependencies":["Decidable.byContradiction","LE.le","LT.lt","Nat","Nat.decLt","Not","OfNat.ofNat","_private.GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialIdentification.0.GinibrePoincare.projected_graph._proof_1","instLENat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialGraph","name":"GinibrePoincare.ginibreFullGenerator_polynomial_graph_iff","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullGenerator_polynomial_basis_graph._proof_2","GinibrePoincare.ginibreFullPolynomialSectorInclusion","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.polynomialSectorGenerator","Iff","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toModule","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.conj_ofReal","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasSum","ContinuousLinearMap.prodMap","DFunLike.coe","Decidable.byContradiction","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMu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","Set.Icc","Set.Ioo","Set.instMembership","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.setLike","Submodule.smulMemClass","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorVariational","name":"GinibrePoincare.ginibreFullGenerator_real_poincare","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullGenerator","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","Inner.inner","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["A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uousSMul","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioo","Set.instMembership","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.addSubmonoidClass","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smul","Submodule.smulMemClass","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHMul","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instTopologicalSpaceSubtype","mul_nonpos_of_nonneg_of_nonpos","real_inner_smul_right","smul_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorVariational","name":"GinibrePoincare.ginibreFullGenerator_real_variational_iff","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHDiv","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","And.left","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Comple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","Real.normedCommRing","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","Zero.toOfNat0","congr","congrArg","fact_one_le_two_ennreal","id","inferInstance","inner_sub_left","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","real_inner_comm","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullGenerator_resolvent_exists","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","EuclideanSpace","Exists","Exists.intro","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullFormGradient","GinibrePoincare.ginibreFullFormOfWeak","GinibrePoincare.ginibreFullFormOfWeak_gradient","GinibrePoincare.ginibreFullFormOfWeak_value","GinibrePoincare.ginibreFullFormResolvent","GinibrePoincare.ginibreFullFormResolvent_riesz","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreFullFormSpace_inner","GinibrePoincare.ginibreFullFormSpace_weak","GinibrePoincare.ginibreFullFormValue","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreFullWeakSpace._proof_4","GinibrePoincare.ginibreFullWeakSpace._proof_5","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdInnerProductSpace","WithLp.instProdSeminormedAddCommGroup","WithLp.instProdTopologicalSpace","congrArg","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullGenerator_resolvent_unique","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullFormGradient","GinibrePoincare.ginibreFullFormResolvent","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreFullFormValue","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommGroup","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullFormGradient","GinibrePoincare.ginibreFullFormOfWeak","GinibrePoincare.ginibreFullFormOfWeak_gradient","GinibrePoincare.ginibreFullFormOfWeak_value","GinibrePoincare.ginibreFullFormResolvent","GinibrePoincare.ginibreFullFormResolvent_riesz","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreFullFormSpace_inner","GinibrePoincare.ginibreFullFormSpace_weak","GinibrePoincare.ginibreFullFormValue","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreFullWeakSpace._proof_4","GinibrePoincare.ginibreFullWeakSpace._proof_5","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne",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_eq_true","rfl","tsupport","tsupport_fderiv_apply_subset"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticUnrestrictedWeakComparison","name":"GinibrePoincare.ginibreFullGradient_fixed_inner_average","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreGradientPermutationAverageL2","GinibrePoincare.ginibreGradientPermutationL2","GinibrePoincare.ginibreMeasure","Inner.inner","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","ContinuousLinearMap.sum_apply","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Equiv.inhabited'","Equiv.instFintype","EuclideanSpace","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype.card","Fintype.card_ne_zero","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreFullGradientPermutation_inner","GinibrePoincare.ginibreGradientPermutationAverageL2","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_1","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_4","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_5","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_6","GinibrePoincare.ginibreGradientPermutationL2","GinibrePoincare.ginibreGradientPermutationL2._proof_13","GinibrePoincare.ginibreGradientPermutationL2._proof_14","GinibrePoincare.ginibreGradientPermutationL2._proof_16","GinibrePoincare.ginibreGradientPermutationL2._proof_19","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2._proof_1","GroupWithZero.toMonoidWithZero","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tAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instAddNat","instHAdd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullHigherMode._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullHigherMode._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullCenteredTransform._proof_2","GinibrePoincare.ginibreFullHigherMode._proof_1","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakModes","name":"GinibrePoincare.ginibreFullHigherMode.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullHigherMode","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","GinibrePoinca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imp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakDeficit","name":"GinibrePoincare.ginibreFullHolomorphicPart.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_10","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_2","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_3","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_4","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_6","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_8","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_9","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_5","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instAddCommMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicPart_continuous","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_2","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_3","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_4","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_6","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicPart_mem_positive","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullHolomorphicPart","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.normedAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","ClosedSubmodule","ClosedSubmodule.instSetLike","ClosedSubmodule.isClosed","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne"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mmRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicRemainder._proof_7","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicRemainder._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_7","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicRemainder._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorNumberTransfer","name":"GinibrePoincare.ginibreFullHolomorphicRemainder.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakDeficit","name":"GinibrePoincare.ginibreFullHolomorphicRemainder.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_10","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_2","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_3","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_4","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_6","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_8","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_9","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_5","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_7","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instAddCommMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullHolomorphicRemainder_continuous","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullHolomorphicRemainder","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarAlgebra.toNormedRing","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","Continuous.comp","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousLinearMap.restrictScalars","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_1","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_10","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_2","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_3","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_4","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_6","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_8","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_9","GinibrePoincare.ginibreFullLpConjugationIsometry","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_5","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreFullL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EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","EuclideanSpace","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreFull_smoothCompact_memLp","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.ginibre_smooth_distributional_gradient","HMul.hMul","HSMul.hSMul","HasCompactSupport","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","LT.lt","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.coeFn_zero_eq","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable.locallyIntegrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsProbabilityMeasure.neZero","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.integrable","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","ae_eq_zero_of_integral_contDiff_smul_eq_zero","congrArg","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instCountableFin","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSMulOfMul","instT6SpaceOfMetrizableSpace","instTopENat","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullLpConjugationIsometry","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","LinearIsometry","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_1","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_2","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_3","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_5","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_7","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","LinearIsometry.mk","LinearMap","LinearMap.mk","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","name":"GinibrePoincare.ginibreFullLpConjugationIsometry._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HAdd.hAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","Semi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ion._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialCompatibility","name":"GinibrePoincare.ginibreFullPolynomialSectorInclusion._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreFullPolynomialSectorInclusion._proof_1","GinibrePoincare.ginibreFullPolynomialSectorInclusion._proof_2","GinibrePoincare.ginibreFullPolynomialSectorInclusion._proof_4","GinibrePoincare.ginibreFullPolynomialSectorInclusion._proof_5","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.subtypeL","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreFull_closedPolynomialSector_le","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnita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ynomialSector","GinibrePoincare.ginibreFullPolynomialSectorInclusion","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.polynomialSectorEigenvector","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealAbs","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealAbs._proof_1","GinibrePoincare.ginibreFullRealAbs._proof_2","GinibrePoincare.ginibreFullSymmetricCompose","GinibrePoincare.ginibreFullSymmetricCompose._proof_1","GinibrePoincare.ginibreFullSymmetricCompose._proof_2","GinibrePoincare.ginibreFullSymmetricCompose._proof_3","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","NNReal","NNReal.instOne","Nat","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealAbs._proof_1","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","NNReal.instOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toPseudoEMetricSpace","Real","Real.metricSpace","Real.normedCommRing","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"],"value_dependencies":["NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","lipschitzWith_one_norm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealAbs._proof_2","type_dependencies":["AddGroup.toSubtractionMonoid","Eq","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Real","Real.instZero","Real.normedCommRing","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0"],"value_dependencies":["NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","norm_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealAbs_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealAbs","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LipschitzWith.coeFn_compLp","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","NNReal","NNReal.instOne","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","lipschitzWith_one_norm","norm_zero"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullRealConstant._proof_1","GinibrePoincare.ginibreFullRealConstant._proof_10","GinibrePoincare.ginibreFullRealConstant._proof_12","GinibrePoincare.ginibreFullRealConstant._proof_2","GinibrePoincare.ginibreFullRealConstant._proof_3","GinibrePoincare.ginibreFullRealConstant._proof_5","GinibrePoincare.ginibreFullRealConstant._proof_6","GinibrePoincare.ginibreFullRealConstant._proof_7","GinibrePoincare.ginibreFullRealConstant._proof_8","GinibrePoincare.ginibreFullRealConstant._proof_9","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_10","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_11","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toModule","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_12","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullRealConstant._proof_1","GinibrePoincare.ginibreFullRealConstant._proof_11","GinibrePoincare.ginibreFullRealConstant._proof_2","GinibrePoincare.ginibreFullRealConstant._proof_3","GinibrePoincare.ginibreFullRealConstant._proof_5","GinibrePoincare.ginibreFullRealConstant._proof_6","GinibrePoincare.ginibreMeasure","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Module.complexToReal","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_3","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_4","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullRealConstant._proof_1","GinibrePoincare.ginibreFullRealConstant._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_7","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_8","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullRealConstant._proof_7","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealConstant","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealConstant","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","name":"GinibrePoincare.ginibreFullRealConstant.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullRealConstant","GinibrePoincare.ginibreFullRealConstant._proof_1","GinibrePoincare.ginibreFullRealConstant._proof_10","GinibrePoincare.ginibreFullRealConstant._proof_12","GinibrePoincare.ginibreFullRealConstant._proof_2","GinibrePoincare.ginibreFullRealConsta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ologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ae","GinibrePoincare.ginibreFullConstant","GinibrePoincare.ginibreFullConstant_ae","GinibrePoincare.ginibreFullRealConstant","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"Gini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em","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullRealEvolution._proof_5","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullRealEvolution._proof_6","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullRealEvolution._proof_7","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullRealEvolution._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullRealEvolution._proof_4","GinibrePoincare.ginibreFullRealEvolution._proof_7","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.ginibreFullRealEvolution._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealEvolution.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupWeakHeat","name":"GinibrePoincare.ginibreFullRealEvolution.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.restrictScalars","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullRealEvolution._proof_1","GinibrePoincare.ginibreFullRealEvolution._proof_10","GinibrePoincare.ginibreFullRealEvolution._proof_12","GinibrePoincare.ginibreFullRealEvolution._proof_13","GinibrePoincare.ginibreFullRealEvolution._proof_16","GinibrePoincare.ginibreFullRealEvolution._proof_17","GinibrePoincare.ginibreFullRealEvolution._proof_2","GinibrePoincare.ginibreFullRealEvolution._proof_3","GinibrePoincare.ginibreFullRealEvolution._proof_4","GinibrePoincare.ginibreFullRealEvolution._proof_5","GinibrePoincare.ginibreFullRealEvolution._proof_6","GinibrePoincare.ginibreFullRealEvolution._proof_8","GinibrePoincare.ginibreFullRealEvolution._proof_9","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullRealEvolution_abs_domination","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Eventually","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealAbs","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.toAddGroup","AddSubgroupClass.toAddSubmonoidClass","AddSubgroupClass.toNegMemClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ref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,"Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulMemClass.continuousSMul","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smulMemClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instTopologicalSpaceSubtype","mul_neg","neg_eq_zero","neg_mul","real_inner_comm","real_inner_self_eq_norm_sq","rfl","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticRealGraphOrbit","name":"GinibrePoincare.ginibreFullRealEvolution_graph_derivative","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instLT","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulMemClass.continuousSMul","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodu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CommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.true","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","Eq","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealAbs","GinibrePoincare.ginibreFullRealAbs_ae","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullRealEvolution_abs_domination","GinibrePoincare.ginibreFullRealEvolution_integral","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Integrable.norm","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.MemLp.integrable","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_mono_ae","Membership.mem","NNReal","Nat","Nat.cast_one","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instLE","Real.instRCLike","Real.instStarOrderedRing","Real.isBoundedSMul","Real.lattice","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","Trans.trans","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instClosedIciTopology","instHasSolidNormReal","instIsOrderedModule","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopologicalSpaceSubtyp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brePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexRe","GinibrePoincare.ginibreFullComplexRe_ofReal","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreFullEvolution_nonneg","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticRealGraphOrbit","name":"GinibrePoincare.ginibreFullRealEvolution_preserves_graph","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup",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onUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.ext","PiLp.innerProductSpace._proof_1","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithLp.instSMul","WithLp.ofLp","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","deriv","dite","eq_false","eq_self","fderiv","id","instCommCStarAlgebraComplex","instContinuousSMulForall","instDecidableEqFin","instDistribOfSemiring","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instTopENat","instZeroENat","ite","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","not_false_eq_true","of_eq_true","smul_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_2","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_3","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_4","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_5","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_6","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.sobolevValueTruncation","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_2","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_4","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_2","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_3","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_4","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.sobolevValueTruncation","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.MemLp","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreValueTruncation_memLp","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.memLp","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","name":"GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_2","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_3","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_4","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_5","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreFullSymmetricValues._proof_4","GinibrePoincare.ginibreFullSymmetricValues._proof_7","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","GinibrePoincare.sobolevValueTruncation","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp.toLp","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_1","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_2","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_3","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_4","GinibrePoincare.ginibreFullSymmetricBoundedTruncation._proof_5","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreFullSymmetricValues._proof_4","GinibrePoincare.ginibreFullSymmetricValues._proof_7","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","GinibrePoincare.ginibreRealPermutationL2_ae","GinibrePoincare.ginibre_measurePreserving_permute","GinibrePoincare.permute","GinibrePoincare.sobolevValueTruncation","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","Semin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dAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricCompose._proof_1","GinibrePoincare.ginibreFullSymmetricCompose._proof_2","GinibrePoincare.ginibreFullSymmetricCompose._proof_3","GinibrePoincare.ginibreFullSymmetricCompose._proof_4","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","LipschitzWith","LipschitzWith.compLp","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","MetricSpace.toEMetricSpace","NNReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullSymmetricCompose._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullSymmetricCompose._proof_2","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupL1","name":"GinibrePoincare.ginibreFullSymmetricCompose._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullSymmetricCompose._proof_1","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup"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roup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullSymmetricIm","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.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onAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexIm_I","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real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omplex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegMemClass.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.toAddGroup","AddSubgroupClass.toAddSubmonoidClass","AddSubgroupClass.toNegMemClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexRe_I","GinibrePoincare.ginibreFullSymmetricIm","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegMemClass.neg","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.module'","Submodule.setLike","Submodule.smul","Subtype","Subtype.ext","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullSymmetricRe_ofReal","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullComplexRe_ofReal","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricRe","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopol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SMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instProdTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricResolvent._proof_2","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricResolvent.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommG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","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.swap","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._proof_1","GinibrePoincare.GinibreFullFormAmbient._proof_2","GinibrePoincare.GinibreFullFormAmbient._proof_3","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullFormOfWeak","GinibrePoincare.ginibreFullFormOfWeak_value","GinibrePoincare.ginibreFullFormResolvent","GinibrePoincare.ginibreFullFormResolvent_riesz","GinibrePoincare.ginibreFullFormSpace","GinibrePoincare.ginibreFullFormValue","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreFullSymmetricValues_orthogonal_weak_eq_zero","GinibrePoincare.ginibreFullValueResolvent","GinibrePoincare.ginibreFullValueResolvent_positive","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.intro","Iff.mp","Iff.mpr","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toMulPosStrictMono","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","Not.intro","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGrou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ue_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricResolvent_eq_zero_iff","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HSub.hSub","Iff.mp","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.setLike","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","map_sub","sub_eq_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","name":"GinibrePoincare.ginibreFullSymmetricResolvent_norm_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseu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mmMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congr","congrArg","contravariant_lt_of_covariant_le","div_pos","fact_one_le_two_ennreal","id","inferInstance","inner_sub_left","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","instTopologicalSpaceSubtype","le_of_lt","mul_nonneg_of_nonpos_of_nonpos","mul_pos_of_neg_of_neg","neg_eq_zero","neg_one_smul","norm_eq_zero","norm_nonneg","real_inner_self_eq_norm_sq","rfl","sq_nonneg","sub_eq_add_neg","sub_eq_zero","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticUnrestrictedWeakComparison","name":"GinibrePoincare.ginibreFullSymmetricResolvent_unrestricted_variational","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","EuclideanSpace","Exists.intro","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullFormAmbient","GinibrePoincare.GinibreFullFormAmbient._pro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AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.instSemilinearIsometryClass","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SemilinearIsometryClass.toSemilinearMapClass","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","map_zero","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.instSemilinearIsometryClass","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instMonoid","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SemilinearIsometryClass.toSemilinearMapClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","map_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues._proof_4","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues._proof_5","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullSymmetricValues._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues._proof_7","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues_complete","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","CompleteSpace","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instUniformSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreFullSymmetricValues_isClosed","GinibrePoincare.ginibreMeasure","IsClosed.completeSpace_coe","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFullSymmetricValues_inner_average","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationAverageL2","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Equiv.inhabited'","Equiv.instFintype","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype.card","Fintype.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ocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","Top.top","True","True.intro","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","fact_one_le_two_ennreal","fderiv","id","instCommCStarAlgebraComplex","instDecidableEqFin","instDecidableTrue","instFintypeProd","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","instZeroENat","ite","ite_congr","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","not_false","not_false_eq_true","of_eq_true","one_div","one_ne_zero._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullTransformedDbar_smooth._proof_1","type_dependencies":["ENat","LE.le","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Top.top","WithTop","WithTop.instPreorder","WithTop.one","WithTop.some","instOneENat","instPreorderENat","instTopENat"],"value_dependencies":["ENat","Eq","Eq.trans","False","LE.le","Ne","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Preorder.toLE","Top.top","True","True.intro","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","eq_false","eq_true","instOneENat","instOrderTopENat","instPreorderENat","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullTransformedDbar_smooth_coefficient","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","EuclideanSpace","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreFullC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Semiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instNatCast","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Real.sqrt","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.left","And.right","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Compl.compl","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instT2Space","Complex.measurableSpace","Complex.ofReal","ContDiff","Continuous","Continuous.comp","Continuous.inner","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","EuclideanSpace","Exists","Exists.casesOn","Field.toDivisionRing","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteCoefficient_eq_inner","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullTransformedDbar","GinibrePoincare.ginibreFullTransformedDbar_smooth_coefficient","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricWeakPair_exists_core_sequence","GinibrePoincare.ginibreTheoremOneNineCorePairs","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_1","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_2","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_3","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_4","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.normalizedVandermondeL2","HAdd.hAdd","HMul.hMul","HasCo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ullComplexOfReal","GinibrePoincare.ginibreFullTransformedDbar_smooth._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.hasCompactSupport_normalizedVandermonde_ofReal","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.smoothCompactL2","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","WithTop.some","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instTopENat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContDiff","ContDiff.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianMeasure_absolutelyContinuous_ginibreMeasure","GinibrePoincare.contDiff_normalizedVandermonde_ofReal","GinibrePoincare.ginibreFullComplexOfReal","GinibrePoincare.ginibreFullComplexOfReal_ae","GinibrePoincare.ginibreFullTransformedDbar_smooth._proof_1","GinibrePoincare.ginibreMassEvaluation","GinibrePoincare.ginibreMeasure","GinibrePoincare.groundStateNormalization","GinibrePoincare.hasCompactSupport_normalizedVandermonde_ofReal","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_coeFn_public","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.normalizedVandermondeTransform_apply","GinibrePoincare.smoothCompactL2","GinibrePoincare.smoothCompactL2_coeFn","GinibrePoincare.vandermonde","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiri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rmedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_19","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullWeakDbar._proof_17","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.ginibreFullWeakDbar._proof_1","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_20","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_21","type_dependencies":["NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","Ring.toSemiring","RingHom.id","RingHomIsometric","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toNonAssocSemiring"],"value_dependencies":["NormedCommRing.toSeminormedCommRing","Real","Real.normedCommRing","RingHomIsometric.ids","SeminormedCommRing.toSeminormedRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_22","type_dependencies":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_23","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instCommCStarAlgebraComplex","instMulZeroClassOfSemiring"],"value_dependencies":["CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedField","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_24","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreFullWeakDbar._proof_10","GinibrePoincare.ginibreFullWeakDbar._proof_12","GinibrePoincare.ginibreFullWeakDbar._proof_13","GinibrePoincare.ginibreFullWeakDbar._proof_23","GinibrePoincare.ginibreFullWeakDbar._proof_5","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulCommClass","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullComplexL2._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Lp.instSMulCommClass","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.norme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ormSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_7","type_dependencies":["AddCommGroup.toAddGroup","CommCStarAlgebra.toNormedCommRing","Complex","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullWeakDbar._proof_5","GinibrePoincare.ginibreFullWeakDbar._proof_7","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.ginibreFullWeakDbar._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.ginibreFullWeakDbar._proof_1","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","Nat","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PiLp","PiLp.normedAddCommGroup","PiLp.normedSpace","Prod","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Rea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Field","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instAdd","PiLp","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.proj","PiLp.proj_apply","PiLp.seminormedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl","smul_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEqualityWeakLinear","name":"GinibrePoincare.ginibreFullWeakEqualitySpace","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoid.mk","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.mk","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.measurableSpace","Continuous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Add","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instMul","Real.instNatCast","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreEquality_weak_variational_iff","GinibrePoincare.ginibreFullCenter","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","HDiv.hDiv","HMul.hMul","Iff.symm","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","With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logicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace._proof_6","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullWeakSpace._proof_4","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup.toContinuousAdd","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","Real.normedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","Prod","Real","Real.normedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","name":"GinibrePoincare.ginibreFullWeakSpace.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","Unifor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ormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instUniformSpaceProd","instUniformSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","CompleteSpace.prod","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreFullWeakSpace_isClosed","GinibrePoincare.ginibreMeasure","IsClosed.completeSpace_coe","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.completeSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instUniformSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","name":"GinibrePoincare.ginibreFullWeakSpace_isClosed","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","IsClosed","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Normed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FullHolomorphicRemainder._proof_3","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_4","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_6","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_8","GinibrePoincare.ginibreFullHolomorphicRemainder._proof_9","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_4","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_5","GinibrePoincare.ginibreFullLpConjugationIsometry._proof_6","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricWeakPair_exists_core_sequence","GinibrePoincare.ginibreTheoremOneNineCorePairs","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_1","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_2","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_3","GinibrePoincare.ginibreTheoremOneNineCorePairs._proof_4","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.transformedCenteredObservableL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsClosed","IsClosed.mem_of_tendsto","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","LinearIsometry","LinearIsometry.continuous","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instMonoid","Real.instRCLike","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","Submodule.starProjection","Subtype","Subtype.val","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","congrArg","congrFun'","continuous_fst","fact_one_le_two_ennreal","funext","id","instArchimedeanNat","instCommCStarAlgebraComplex","instFintypeProd","instHPow","instInhabitedNat","instInnerProductSpaceRealComplex","instIsDirectedOrder","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","isClosed_eq","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFull_L2_sum_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","Finset","Finset.sum","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalR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ealComplex","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","EuclideanDomain.toMulDivCancelClass","Field.toEuclideanDomain","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreLebesgueDensityReal_ne_zero_ae","GinibrePoincare.ginibreMeasure","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommMonoidWithZero","Real.instDivInvMonoid","Real.instField","Real.instMul","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","id","instCommCStarAlgebraComplex","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","mul_div_cancel_left\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorCoreCompatibility","name":"GinibrePoincare.ginibreFull_distributional_density_pairing","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreMeasure","HDiv.hDiv","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.integral","Membership.mem","Nat","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithLp.ofLp","WithTop.some","fact_one_le_two_ennreal","fderiv","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAd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inormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHMul","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instStarRing","Complex.instSub","Complex.measurableSpace","Complex.norm_real","Complex.ofReal","Continuous","Continuous.aestronglyMeasurable","Continuous.const_mul","Continuous.fun_sub","Continuous.mul","Continuous.norm","Continuous.pow","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.continuous","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toMulAction","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.univ_mem'","Fin","Fin.fintype","Fin.instOfNat","Finset","Finset.instSetLike","Finset.sum","Finset.univ","Finsupp","Finsupp.instAdd","Finsupp.instAddZeroClass","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.complexRadius","GinibrePoincare.coordinateSum","GinibrePoincare.differentiable_sumRadiusPolynomial","GinibrePoincare.ginibreFull_centeredScaled_norm_sq_le","GinibrePoincare.ginibreFull_sumRadiusPolynomial_memLp","GinibrePoincare.ginibreMeasure","GinibrePoincare.pairwiseRadius","GinibrePoincare.sumRadiusCoordinate","GinibrePoincare.sumRadiusPolynomial","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Comm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minormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","TopologicalSpace","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithLp.ofLp","autoParam","congrArg","congrFun'","eq_of_heq","eq_self","fact_one_le_two_ennreal","fderiv","funext","id","instAddNat","instCommCStarAlgebraComplex","instContinuousSMulForall","instDecidableEqFin","instFintypeProd","instHAdd","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLENat","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","noConfusion_of_Nat","one_ne_zero._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialGradient","name":"GinibrePoincare.ginibreFull_polynomial_realDirection_memLp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.realCoordinateDirection","GinibrePoincare.sumRadiusPolynomial","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp","MvPolynomial","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Derivation","Derivation.instFunLike","Distrib.leftDistribClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENorm","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","ESeminormedAddMonoid.toContinuousENorm","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_ite_eq'","Finset.univ","Finsupp","Finsupp.instAddCommMonoid","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.complexRadius","GinibrePoincare.coordinateSum","GinibrePoincare.fderiv_sumRadiusPolynomial","GinibrePoincare.ginibreFull_polynomial_centered_memLp","GinibrePoincare.ginibreFull_polynomial_conj_centered_memLp","GinibrePoincare.ginibreFull_sumRadiusPolynomial_memLp","GinibrePoincare.ginibreMeasure","GinibrePoincare.radius_gradient_real","GinibrePoincare.realCoordinateDirection","GinibrePoincare.sumRadiusPolynomial","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.add","Membership.mem","MonoidHomClass.toOneHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MvPolynomial","MvPolynomial.pderiv","Nat","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonAssocSemiring.toMulZeroOneClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toENormedAddCommMonoid","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instAdd","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congr","congrArg","congrFun'","eq_of_heq","eq_self","fderiv","funext","id","instCommCStarAlgebraComplex","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","instLENat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","ite","ite_eq_left_of_eq_true","map_one","mul_add","mul_one","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorSpectrum","name":"GinibrePoincare.ginibreFull_positive_contraction_spectrum","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.IsPositive","ContinuousLinearMap.algebra","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.ring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","LE.le","Module.toDistribMulAction","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instLE","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","And.intro","CStarAlgebra.toNormedAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","CompletelyNormalSpace.toNormalSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instDenselyNormedField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eq_self","fact_one_le_two_ennreal","fderiv","fderiv_of_notMem_tsupport","funext","instCountableFin","instDecidableEqFin","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSigmaCompactSpaceForallOfFinite","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","isClosed_tsupport","ite","ite_congr","ite_self","locallyCompact_of_proper","of_eq_true","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable","tsupport","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDensity","name":"GinibrePoincare.ginibreFull_smoothCompact_symmetric_pair","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","EuclideanSpace","Exists","Exists.intro","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.IsGinibreSymmetricWeakPair._proof_1","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.IsSymmetric","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_comp_permute","GinibrePoincare.ginibreFullWeakSpace","GinibrePoincare.ginibreFullWeakSpace._proof_4","GinibrePoincare.ginibreFullWeakSpace._proof_5","GinibrePoincare.ginibreFull_smoothCompact_memLp","GinibrePoincare.ginibreGradientPermutationL2","GinibrePoincare.ginibreGradientPermutationL2._proof_13","GinibrePoincare.ginibreGradientPermutationL2._proof_14","GinibrePoincare.ginibreGradientPermutationL2._proof_16","GinibrePoincare.ginibreGradientPermutationL2._proof_19","GinibrePoincare.ginibreGradientPermutationL2_ae","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2","GinibrePoincare.ginibreRealPermutationL2._proof_1","GinibrePoincare.ginibreRealPermutationL2_ae","GinibrePoincare.ginibre_measurePreserving_permute","GinibrePoincare.ginibre_smooth_distributional_gradient","GinibrePoincare.permute","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","WithLp.toLp","WithTop.some","congrArg","fact_one_le_two_ennreal","funext","id","instFintypeProd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialMoments","name":"GinibrePoincare.ginibreFull_sumRadiusPolynomial_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.sumRadiusPolynomial","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp","MvPolynomial","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMet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","HPow.hPow","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHMul","instHPow","instLENat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommMagma.toMul","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.continuous_conj","Complex.continuous_normSq","Complex.continuous_ofReal","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.measurableSpace","Complex.normSq","Complex.normSq_nonneg","Complex.norm_conj","Complex.norm_real","Complex.ofReal","Continuous","Continuous.aestronglyMeasurable","Continuous.comp'","Continuous.fun_pow","Continuous.fun_sub","Continuous.prodMk","ContinuousENorm","ContinuousENorm.toENorm","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.instSetLike","Finset.sum","Finset.sum_nonneg","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreFull_polynomial_joint_moment_integrable","GinibrePoincare.ginibreMeasure","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.memLp_two_iff_integrable_sq_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toR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o.toOfNat0","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instSecondCountableTopologyReal","instTopologicalSpaceSubtype","measurable_fst","measurable_snd","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianProjection","name":"GinibrePoincare.ginibreGaussianNoise_center_recenter_independent","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.IsBrownianVectorProcess","GinibrePoincare.ginibreCenterProjectionEuclidean","GinibrePoincare.ginibreRecenterProjectionEuclidean","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MetricSpace.toEMetricSpace","NNReal","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PiLp.topologicalSpace","PolishSpace.toSecondCountableTopology","ProbabilityTheory.IndepFun","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.measurableSpace","fact_one_le_two_ennreal","instCountableFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","secondCountable_of_proper"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.GinibreRealEuclidean","GinibrePoincare.GinibreRealEuclidean._proof_1","GinibrePoincare.IsBrownianVectorProcess","GinibrePoincare.IsBrownianVectorProcess.toIsGaussianProcessWithBrownianCovariance","GinibrePoincare.ginibreCenterProjectionEuclidean","GinibrePoincare.ginibreCenterProjectionEuclidean_selfAdjoint","GinibrePoincare.ginibreCenterRecenterEuclidean_orthogonal","GinibrePoincare.ginibreRecenterProjectionEuclidean","GinibrePoincare.ginibreRecenterProjectionEuclidean_selfAdjoint","GinibrePoincare.orthogonalGaussianProjections_indepFun","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MetricSpace.toEMetricSpace","NNReal","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","fact_one_le_two_ennreal","instCountableFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticGaussi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ow","NNReal","NNReal.instSemiring","NNReal.mk","NPow.toPow","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instMul","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.semiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instOfNatNat","sq_nonneg"],"value_dependencies":["AEMeasurable.add_const","AEMeasurable.const_mul","AEMeasurable.fst","AddGroup.existsAddOfLE","AddMonoid.toAddZeroClass","CommRing.toNonUnitalCommRing","ContinuousAdd.measurableAdd","ContinuousMul.measurableMul","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Function.comp","HAdd.hAdd","HMul.hMul","HPow.hPow","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Lattice.toSemilatticeInf","Measurable.add_const","Measurable.aemeasurable","Measurable.const_mul","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.map","MeasureTheory.Measure.map_map","MeasureTheory.Measure.prod","MeasureTheory.MeasurePreserving.map_eq","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.measurePreserving_fst","MeasureTheory.measurePreserving_snd","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instSemiring","NNReal.mk","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Preorder.toLE","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.IndepFun","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_add_gaussianReal_of_indepFun","ProbabilityTheory.gaussianReal_map_add_const","ProbabilityTheory.gaussianReal_map_const_mul","ProbabilityTheory.indepFun_prod","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instMul","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","aemeasurable_id","congrArg","congrFun'","eq_self","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatNat","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurable_fst","measurable_id","measurable_id'","measurable_snd","of_eq_true","rfl","sq_nonneg","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticGaussianFourthMoment","name":"GinibrePoincare.ginibreGaussian_centered_fourthMoment","type_dependencies":["Eq","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.gaussianReal","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableS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onglyMeasurable_id","congrArg","instHAdd","instHPow","instIsTopologicalRingReal","instOfNatNat","instSecondCountableTopologyReal","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticGaussianSquareMoments","name":"GinibrePoincare.ginibreGaussian_hasLaw_square_memLp_two","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","HPow.hPow","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.MemLp","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.gaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instZero","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","ContinuousENorm.toENorm","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.mp","Eq.symm","Function.comp","GinibrePoincare.ginibreGaussian_square_memLp_two","HPow.hPow","Iff.mp","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.AEStronglyMeasurable.fun_pow","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.memLp_map_measure_iff","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.gaussianReal","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instMonoid","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aestronglyMeasurable_id","congrArg","instHPow","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticGaussianSquareMoments","name":"GinibrePoincare.ginibreGaussian_hasLaw_square_variance","type_dependencies":["Eq","HMul.hMul","HPow.hPow","MeasurableSpace","MeasureTheory.Measure","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.gaussianReal","ProbabilityTheory.variance","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AEMeasurable.pow_const","CommRing.toNonUnitalCommRing","ContinuousMul.measurableMul\u2082","Eq","Eq.mp","Eq.symm","Function.comp","GinibrePoincare.ginibreGaussian_square_variance","HMul.hMul","HPow.hPow","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.map","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instMeasurableSpace","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.gaussianReal","ProbabilityTheory.variance","ProbabilityTheory.variance_map","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","aemeasurable_id","congrArg","instHMul","instHPow","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianCoordinateLaw","name":"GinibrePoincare.ginibreGaussian_product_curry","type_dependencies":["DFunLike.coe","Eq","EquivLike.toFunLike","Fintype","MeasurableEquiv","MeasurableEquiv.curry","MeasurableEquiv.instEquivLike","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","Prod","instFintypeProd"],"value_dependencies":["CommSemiring.toCommMonoid","DFunLike.coe","ENNReal","ENNReal.instCommSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Equiv.curry","Equiv.curry_symm_apply","Equiv.symm","EquivLike.toFunLike","Finite.of_fintype","Finite.to_countable","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.univ","Fintype","Fintype.prod_prod_type","Function.comp","Function.uncurry","Iff","MeasurableEquiv","MeasurableEquiv.apply_symm_apply","MeasurableEquiv.curry","MeasurableEquiv.curry._proof_2","MeasurableEquiv.curry._proof_4","MeasurableEquiv.curry.eq_1","MeasurableEquiv.instEquivLike","MeasurableEquiv.measurable","MeasurableEquiv.mk","MeasurableEquiv.symm","MeasurableSet","MeasurableSet.univ_pi","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.map_id'","MeasureTheory.Measure.map_map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.Measure.pi_eq","MeasureTheory.Measure.pi_pi","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Membership.mem","Prod","Prod.forall._simp_1","Prod.mk","Set","Set.ext","Set.instMembership","Set.mem_pi._simp_1","Set.mem_preimage._simp_1","Set.mem_univ._simp_1","Set.pi","Set.preimage","Set.univ","SetLike.instMembership","True","congr","congrArg","congrFun'","eq_self","forall_congr","forall_const._simp_1","funext","id","iff_self","implies_congr","instCountableProd","instFintypeProd","instInhabitedTrue","instNonemptyOfInhabited","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUQuadraticConditional","name":"GinibrePoincare.ginibreGaussian_product_radius_integral","type_dependencies":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","MeasureTheory.Measure.prod","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.gaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Function.comp","GinibrePoincare.ginibreGaussian_secondMoment","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.T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CoreClosureEquivalence","name":"GinibrePoincare.ginibreGlobalRealSmoothPairs._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRealCoreClosureEquivalence","name":"GinibrePoincare.ginibreGlobalRealSmoothPairs._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRealCoreClosureEquivalence","name":"GinibrePoincare.ginibreGlobalRealSmoothPairs._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRealCoreClosureEquivalence","name":"GinibrePoincare.ginibreGlobalRealSmoothPairs._proof_4","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.OuterMeasureClass","Nat"],"value_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.Measure.instOuterMeasureClass","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreGradedClosedSpan_eq_degreeZero_sup_positive","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","ClosedSubmodule","ClosedSubmodule.instMax","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGr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oid","SetLike.instMembership","Subtype","T5Space.toT1Space","T6Space.toT5Space","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","iSup_le","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instT6SpaceOfMetrizableSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreWeakPermutation","name":"GinibrePoincare.ginibreGradientCoordinateEquiv","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.ParticlePermutation","LinearIsometryEquiv","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","Prod","Real","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv.prodCongr","Equiv.refl","Fin","Fin.fintype","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreRealPermutationL2._proof_1","LinearIsometryEquiv.piLpCongrLeft","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Prod","Real","Real.normedCommRing","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreWeakPermutation","name":"GinibrePoincare.ginibreGradientPermutationAverageL2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.instSMul","DistribMulAction.toDistribSMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv.instFintype","EuclideanSpace","Fin","Fin.fintype","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_1","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_4","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_5","GinibrePoincare.ginibreGradientPermutationAverageL2._proof_6","GinibrePoincare.ginibreGradientPermutationL2","GinibrePoincare.ginibreGradientPermutationL2._proof_13","GinibrePoincare.ginibreGradientPermutationL2._proof_14","GinibrePoincare.ginibreGradientPermutationL2._proof_16","GinibrePoincare.ginibreGradientPermutationL2._proof_19","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealPermutationL2._proof_1","HSMul.hSMul","Inv.inv","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instDecidableEqFin","instFintypeProd","instHSMul","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakPermutation","name":"GinibrePoincare.ginibreGradientPermutationAverageL2._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreGradientPermutationL2._proof_13","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakPermutation","name":"GinibrePoincare.ginibreGradientPermutationAverageL2._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsT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ormSq","GinibrePoincare.ginibreHamiltonianGradientNormSq","GinibrePoincare.ginibreInteractionGradientNormSq","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instAdd","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","instHAdd","instHMul","instHPow","instHSub","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toAdd","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instSub","Complex.mul_re","Complex.normSq","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.coordinateDirection","GinibrePoincare.fderiv_configurationNormSq_coordinate","GinibrePoincare.fderiv_ginibreHamiltonian_coordinate","GinibrePoincare.fderiv_ginibreInteractionPotential_coordinate","GinibrePoincare.fderiv_ginibreInteractionPotential_radial","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianGradientNormSq","GinibrePoincare.ginibreInteractionGradientNormSq","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.ginibreRealCoordinateDifferential_radial","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Mathlib.Tactic.RingNF.add_assoc_rev","Mathlib.Tactic.RingNF.int_rawCast_neg","Mathlib.Tactic.RingNF.mul_assoc_rev","Mathlib.Tactic.RingNF.mul_neg","Mathlib.Tactic.RingNF.nat_rawCast_1","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.instAddMonoid","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMonoid","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","No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ub","instMulNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.continuous","Continuous.comp_continuousOn","ContinuousOn","ContinuousOn.comp","ContinuousOn.intervalIntegrable_of_Icc","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.ginibreHamiltonianGradientNormSq","GinibrePoincare.ginibreHamiltonianGradientNormSq_interaction","GinibrePoincare.ginibreInteractionGradientNormSq","GinibrePoincare.ginibreInteractionGradientNormSq_continuousOn","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IntervalIntegrable","IntervalIntegrable.const_mul","IntervalIntegrable.sub","LE.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNormedRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instCompleteSpace","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.locallyFinite_volume","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUni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TopENat","instTopologicalSpaceNat","intervalIntegral","intervalIntegral.integral_congr","isOpen_lt","le_of_lt","metricSpacePi","min_eq_left","min_le_right","neg_lt_neg","nhds","of_eq_true","propext","rfl","secondCountable_of_proper","stronglyMeasurable_of_tendsto","tendsto_const_nhds","tendsto_pi_nhds","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOUSublevelInteractionDensity","name":"GinibrePoincare.ginibreHamiltonianOU_sublevel_interaction_action_density_exists","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.toSMul","And","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Continuous","ContinuousENorm.toENorm","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.atTop","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.brownianVectorExponentialIntegralDensity","GinibrePoincare.ginibreBrownianAugmentedFiltration","GinibrePoincare.ginibreConfigurationBrownianNoise","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianGradientPathWeight","GinibrePoincare.ginibreHamiltonianOUReferenceProcess","GinibrePoincare.ginibreHamiltonianOUSublevelStop","GinibrePoincare.ginibreInteractionBrownianTilt","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.ginibreQuadraticGradientPathWeight","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsCompact","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsStoppingTime","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.StronglyAdapted","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","MetricSpace.toEMetricSpace","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.toIsPreBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.exp","Real.instDivInvMonoid","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Ring.toSemiring","Semifield.toCommSemiring","SemilatticeInf.toMin","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Set","Set.instMembership","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","WithTop.some","Zero.toOfNat0","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHDiv","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.toSMul","And","And.casesOn","And.intro","And.left","And.right","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Continuous","Continuous.comp","Continuous.continuousOn","ContinuousENorm.toENorm","ContinuousOn","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSe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,"GinibrePoincare.gaussianWeight","GinibrePoincare.ginibreHamiltonianSublevel","GinibrePoincare.ginibreHamiltonianSublevel_eq_weight_superlevel","GinibrePoincare.ginibreWeight","GinibrePoincare.vandermondeWeight","HMul.hMul","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsClosed","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toRing","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.lattice","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.ofPred","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","congrArg","contDiff_const","continuous_const","id","instDistribOfSemiring","instHMul","instHasSolidNormReal","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instTopENat","isClosed_le"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianSublevels","name":"GinibrePoincare.ginibreHamiltonianSublevel_isCompact","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonianSublevel","IsCompact","LT.lt","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And.left","And.right","Bool","Bool.false","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNorm","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.instZero","Complex.normSq","Complex.normSq_eq_norm_sq","Complex.normSq_nonneg","DFunLike.coe","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mem_univ","Finset.single_le_sum","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianLowerBoundConstant","GinibrePoincare.ginibreHamiltonianSublevel","GinibrePoincare.ginibreHamiltonianSublevel_isClosed","GinibrePoincare.ginibreHamiltonian_quadratic_lower_bound","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsCompact.of_isClosed_subset","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Met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mRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_nonneg","addRightReflectLE_of_addLeftReflectLE","cast","congrArg","congrFun'","contravariant_lt_of_covariant_le","dist_zero_right","div_pos","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","le_abs_self","le_div_iff\u2080","le_of_lt","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","neg_neg_of_pos","norm_nonneg","pi_norm_le_iff_of_nonneg","pi_properSpace","propext","pseudoMetricSpacePi","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGradientPathMeasure","name":"GinibrePoincare.ginibreHamiltonian_action_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonian","Measurable","MeasurableSpace.pi","Nat","Real","Real.measurableSpace"],"value_dependencies":["BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff.continuous","Continuous.measurable","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub\u2082","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.vandermondeWeight","HMul.hMul","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.comp","Measurable.mul","Measurable.sub","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddGroup","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.log","Real.measurableSpace","Real.measurable_log","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","id","instCommCStarAlgebraComplex","instCountableFin","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopENat","measurable_const","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianActualStationaryOUReversal","name":"GinibrePoincare.ginibreHamiltonian_actual_stationary_OU_horizon_reverse","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousMap","ContinuousMap.comp","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.ginibreActualStationaryOU_configMeasurable","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreHamiltonianCompactReverseTime","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreHamiltonianOUJointHorizonPath","HDiv.hDiv","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","Membership.mem","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemiring","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHDiv","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AEMeasurable","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","Continuous.measurable","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousMap","ContinuousMap.comp","ContinuousMap.compactOpen","ContinuousMap.continuous_precomp","ContinuousMap.instSecondCountableTopology","DFunLike.coe","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreContinuousNoise","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance1","GinibrePoincare.GinibreHamiltonianConfigurationOUReference_instance3","GinibrePoincare.ginibreActualStationaryOU_configBorel","GinibrePoincare.ginibreActualStationaryOU_configMeasurable","GinibrePoincare.ginibreActualStationaryOU_scalarBorel","GinibrePoincare.ginibreActualStationaryOU_scalarMeasurable","GinibrePoincare.ginibreBrownianFullContinuousNoise","GinibrePoincare.ginibreBrownianOUHorizonPath","GinibrePoincare.ginibreBrownianOUHorizonPath_measurable","GinibrePoincare.ginibreBrownianOU_stationary_continuous_horizon_law_reversal","GinibrePoincare.ginibreConfigurationOUAssemble","GinibrePoincare.ginibreConfigurationOUAssemble_measurable","GinibrePoincare.ginibreConfigurationOUAssemble_reverse","GinibrePoincare.ginibreHamiltonianCompactReverseTime","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreHamiltonianOUJointHorizonPath","GinibrePoincare.ginibreHamiltonianOUReference_horizon_scalar_assembly","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.ginibreScalarOUHorizon_independent_coordinates","GinibrePoincare.ginibreScalarOUPairHorizonMeasurable","GinibrePoincare.instMeasurableSpaceContinuousMapElemNNRealIccOfNatReal_ginibrePoincare","HDiv.hDiv","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.of_eval","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.Measure.map_congr","MeasureTheory.Measure.map_map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi_map_pi","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instDiv","NNReal.instOne","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instSecondCountableTopology","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCom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"GinibrePoincare.ginibreHamiltonianKilledOUActionWeight_reverse","GinibrePoincare.ginibreHamiltonianOUCoordinateAssembly","GinibrePoincare.ginibreHamiltonianOUJointHorizonPath","GinibrePoincare.ginibreHamiltonian_actual_stationary_OU_horizon_reverse","GinibrePoincare.invariant_measure_withDensity_of_invariant_weight","HDiv.hDiv","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable.comp","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.map","MeasureTheory.Measure.withDensity","Membership.mem","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemiring","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instHDiv","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianCoercivity","name":"GinibrePoincare.ginibreHamiltonian_bounded_below","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianLowerBoundConstant","LE.le","LT.lt","Nat","Neg.neg","OfNat.ofNat","Real","Real.instLE","Real.instNeg","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.configurationNormSq_nonneg","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonianLowerBoundConstant","GinibrePoincare.ginibreHamiltonian_quadratic_lower_bound","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Math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","Finset.instSetLike","Finset.mem_erase","Finset.mem_univ","Finset.single_le_sum","Finset.sum","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.Injective","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonian_real_configuration_imaginary_hessian","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.secondDirectionalDerivative","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.pow_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","Mul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","id","inferInstance","instAddNat","instDecidableEqFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianItoGenerator","name":"GinibrePoincare.ginibreHamiltonian_ito_generator","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.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","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","NSMul.toSMul","Nat","Nat.cast","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Real","Real.instAdd","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRing","Real.semiring","Ring.toAddGroupWithOne","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Zero.toOfNat0","congrArg","congrFun'","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","nsmul_eq_mul","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianPrefix","name":"GinibrePoincare.ginibreHamiltonian_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonian","Measurable","MeasurableSpace.pi","Nat","Real","Real.measurableSpace"],"value_dependencies":["BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff.continuous","Continuous.measurable","ContinuousMul.measurableMul\u2082","ContinuousSub.measurableSub\u2082","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.vandermondeWeight","HMul.hMul","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable.comp","Measurable.mul","Measurable.sub","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddGroup","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.log","Real.measurableSpace","Real.measurable_log","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","instCommCStarAlgebraComplex","instCountableFin","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopENat","measurable_const","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOriginalKilledInitialIntegration","name":"GinibrePoincare.ginibreHamiltonian_original_killed_gaussian_initial_identity","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousMap","DFunLike.coe","ENNReal.ofReal","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreGaussianInitialOUPath","GinibrePoincare.ginibreGaussianInitialOriginalPath","GinibrePoincare.ginibreHamiltonianCompactSurvival","GinibrePoinca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inuousNeg","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","Measurable","Measurable.comp","Measurable.neg","MeasurableSet","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.ae","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.sigmaFinite_of_locallyFinite","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.borelSpace","Pi.instNeg","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instLE","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.log","Real.measurableSpace","Real.measurable_exp","Real.measurable_log","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instMembership","Set.ofPred","Subtype","Subtype.mk","Subtype.property","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyMetrizableSpace.toIsCompletelyPseudoMetrizableSpace","TopologicalSpace.PseudoMetrizableSpace.regularSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","True.intro","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_false","eq_self","eq_true","funext","id","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instDistribOfSemiring","instFintypeProd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instProperSpaceReal","instR1Space","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopENat","instTopologicalSpaceSubtype","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","not_false_eq_true","of_eq_true","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePointwiseCurvatureTangent","name":"GinibrePoincare.ginibreHamiltonian_pair_direction_le","type_dependencies":["Complex.ofReal","Fin","Function.Injective","GinibrePoincare.ginibreCurvaturePairDirection","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.secondDirectionalDerivative","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instN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d","Filter","Filter.Eventually","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.ginibreHamiltonian","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","And","And.intro","CommRing.toNonUnitalCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.continuous","Continuous.continuousAt","ContinuousAt.tendsto","DenselyNormedField.toNontriviallyNormedField","DistribLattice.toLattice","ENat","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Tendsto","Filter.Tendsto.add_atTop","Filter.Tendsto.comp","Filter.Tendsto.mul","Filter.atBot","Filter.atTop","Filter.tendsto_neg_atBot_atTop","Fin","Fin.fintype","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermondeWeight_eq_zero_iff","GinibrePoincare.vandermondeWeight_pos_of_collisionFree","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","Iff.mpr","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Lattice.toSemilatticeInf","Membership.mem","Nat","Nat.cast","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instZero","Real.linearOrder","Real.log","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.tendsto_log_nhdsGT_zero","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Ioi","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","eq_of_heq","funext","instDistribLatticeOfLinearOrder","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOrderTopologyReal","instTopENat","nhds","nhdsWithin","sub_eq_add_neg","tendsto_const_nhds","tendsto_nhdsWithin_iff"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUni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asureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreHolomorphicAmbientClosedSpan_eq_graded","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.in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reHolomorphicPhaseDegree_orthogonal","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHolomorphicPhaseDegree","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule.IsOrtho","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHolomorphicPhaseDegree","GinibrePoincare.ginibreMeasure","GinibrePoincare.inner_eq_zero_of_ginibre_phase_degrees_ne","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Ne.symm","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreHolomorphicProjection_mem_divisibleEntire","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireL2","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireL2","GinibrePoincare.ginibreDivisibleEntireL2_eq_holomorphicAmbient","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRin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rePoincare.ginibreIndependent_condDistrib","type_dependencies":["DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Filter.EventuallyEq","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instCompleteSpace","Real.instInhabited","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","instNonemptyOfInhabited","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","standardBorel_of_polish"],"value_dependencies":["EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Measurable","Measurable.aemeasurable","MeasurableSpace","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.compProd","MeasureTheory.Measure.compProd_const","MeasureTheory.Measure.instSFiniteMap","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.map_prod_eq_prod_map_map","ProbabilityTheory.IndepFun.symm","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.const.instIsFiniteKernel","ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instCompleteSpace","Real.instInhabited","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","congrArg","id","instNonemptyOfInhabited","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","standardBorel_of_polish"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticConditionalKernel","name":"GinibrePoincare.ginibreIndependent_condDistrib_general","type_dependencies":["DFunLike.coe","Filter.EventuallyEq","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Nonempty","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","StandardBorelSpace"],"value_dependencies":["Eq","Eq.mpr","Eq.refl","Measurable","Measurable.aemeasurable","MeasurableSpace","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.compProd","MeasureTheory.Measure.compProd_const","MeasureTheory.Measure.instSFiniteMap","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","Nonempty","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.map_prod_eq_prod_map_map","ProbabilityTheory.IndepFun.symm","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.const.instIsFiniteKernel","ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd","Prod","Prod.instMeasurableSpace","Prod.mk","StandardBorelSpace","congrArg","id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticPredictableInnovation","name":"GinibrePoincare.ginibreIndependent_predictable_centered_conditional","type_dependencies":["Eq","Filter.EventuallyEq","HMul.hMul","InnerProductSpace.toNormedSpace","Measurable","MeasurableSpace","MeasurableSpace.comap","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.integral","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","StandardBorelSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","inferInstance","instHMul"],"value_dependencies":["BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousMul.measurableMul\u2082","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.EventuallyEq.trans","Filter.mp_mem","Filter.univ_mem'","Function.comp","GinibrePoincare.ginibreIndependent_condDistrib_general","HMul.hMul","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.mul","Measurable.stronglyMeasurable","MeasurableSpace","MeasurableSpace.comap","MeasureTheory.Integrable","MeasureTheory.Integrable.comp_aemeasurable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.ae","MeasureTheory.ae_of_ae_map","MeasureTheory.condExp","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integral","MeasureTheory.integral_const_mul","Membership.mem","MetricSpace.toEMetricSpace","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Nonempty","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toNormSMulClass","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.map_eq","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.integrable_mul","ProbabilityTheory.IndepFun.symm","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.const","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.condDistrib","ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.commRing","Real.instCompleteSpace","Real.instMul","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Set","Set.instMembership","Set.ofPred","StandardBorelSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instENormSMulClass","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instSMulOfMul","instSecondCountableTopologyReal","measurable_fst","measurable_snd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticPredictableInnovation","name":"GinibrePoincare.ginibreIndependent_predictable_memLp_two","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","HMul.hMul","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","Mea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ormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.aemeasurable","ProbabilityTheory.HasLaw.integral_comp","ProbabilityTheory.IndepFun","ProbabilityTheory.IndepFun.comp","ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral","ProbabilityTheory.IndepFun.symm","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instCommMonoid","Real.instMonoid","Real.instMul","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","UniformSpace.toTopologicalSpace","congrArg","congrFun'","funext","id","instDistribOfSemiring","instHMul","instHPow","instIsTopologicalRingReal","instOfNatNat","instSecondCountableTopologyReal","mul_pow"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","name":"GinibrePoincare.ginibreInitialCollisionEmbedding","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","MeasurableEmbedding","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace","Subtype.val"],"value_dependencies":["BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","Eq","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.isOpen_collisionFree","IsOpen.measurableSet","MeasurableEmbedding.subtype_coe","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.ofPred","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instCountableFin","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","name":"GinibrePoincare.ginibreInitialCollisionNormalization_nonempty","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","Nat","Nonempty","Subtype"],"value_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCollisionFreeDefault","Nat","Nonempty.intro","Subtype"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","name":"GinibrePoincare.ginibreInitialCollisionNormalize","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","Nat","Subtype"],"value_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInitialCollisionEmbedding","GinibrePoincare.ginibreInitialCollisionNormalization_nonempty","MeasurableEmbedding.invFun","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace","Subtype.val"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","name":"GinibrePoincare.ginibreInitialCollisionNormalize_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInitialCollisionNormalize","Measurable","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace"],"value_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInitialCollisionEmbedding","GinibrePoincare.ginibreInitialCollisionNormalization_nonempty","MeasurableEmbedding.measurable_invFun","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace","Subtype.val"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","name":"GinibrePoincare.ginibreInitialCollisionNormalize_of_free","type_dependencies":["Eq","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInitialCollisionNormalize","Nat","Subtype","Subtype.mk"],"value_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInitialCollisionEmbedding","GinibrePoincare.ginibreInitialCollisionNormalization_nonempty","MeasurableEmbedding.leftInverse_invFun","MeasurableSpace.pi","Nat","Subtype","Subtype.instMeasurableSpace","Subtype.mk","Subtype.val"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","name":"GinibrePoincare.ginibreInteractionBrownianTilt","type_dependencies":["Fin","GinibrePoincare.Configuration","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreInteractionBrownianTilt._proof_1","GinibrePoincare.ginibreInteractionPotential","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","name":"GinibrePoincare.ginibreInteractionBrownianTilt._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","name":"GinibrePoincare.ginibreInteractionBrownianTilt_compact_bound","type_dependencies":["And","CommCStarAlgebra.toNormedCommRing","Complex","Exists","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionBrownianTilt","HPow.hPow","IsCompact","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instFintypeProd","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.casesOn","And.intro","Bornology.IsBounded.exists_pos_norm_le","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","ContinuousOn","ContinuousOn.mono","ContinuousOn.pow","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","GT.gt","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionBrownianTilt","GinibrePoincare.ginibreInteractionBrownianTilt_continuousOn","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact","IsCompact.image_of_continuousOn","IsCompact.isBounded","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le",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Monoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.ginibreConfigurationBrownianGradientSum","GinibrePoincare.ginibreConfigurationBrownianGradientSum_eq","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreInteractionBrownianTilt","GinibrePoincare.ginibreInteractionBrownianTilt._proof_1","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.itoUniformNNTime","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Rat.rawCast","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instRing","Real.instSub","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fderiv","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","name":"GinibrePoincare.ginibreInteractionBrownianTilt_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionBrownianTilt","Measurable","MeasurableSpace.pi","Nat","OfNat.ofNat","Prod","Real","Real.measurableSpace","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousMul.measurableMul\u2082","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreInteractionBrownianTilt._proof_1","GinibrePoincare.ginibreInteractionPotential","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable.mul","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.sqrt","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instCountableFin","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurable_const","measurable_fderiv_apply_const","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","name":"GinibrePoincare.ginibreInteractionBrownianTilt_noise_drift","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreInteractionBrownianTilt","GinibrePoincare.ginibreInteractionPotential","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedFiel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roup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.Function.module","Pi.addCommGroup","Pi.instPow","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","continuousOn_finset_sum","continuous_const","fderiv","id","instCommCStarAlgebraComplex","instHAdd","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","not_false_eq_true","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","name":"GinibrePoincare.ginibreInteractionPotential","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.vandermondeWeight","Nat","Neg.neg","Real","Real.instNeg","Real.log"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialDensityCancellation","name":"GinibrePoincare.ginibreInteractionPotential.eq_1","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionPotential","GinibrePoincare.vandermondeWeight","Nat","Neg.neg","Real","Real.instNeg","Real.log"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionPotential","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","name":"GinibrePoincare.ginibreInteractionPotential_contDiffAt","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiffAt","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreInteractionPotential","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.contDiffAt","ContDiffAt.log","ContDiffAt.neg","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.contDiff_vandermondeWeight","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermondeWeight_pos_of_collisionFree","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instPreorder","Real.instRCLike","Real.instZero","Real.log","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","Zero.toOfNat0","instInnerProductSpaceRealComplex","instTopENat","ne_of_gt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","name":"GinibrePoincare.ginibreInteractionPotential_coordinate_hessian","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instInv","Complex.instMul","Complex.instSub","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNor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LampertiGenerator","name":"GinibrePoincare.ginibreLampertiCenterDrift_measurable","type_dependencies":["GinibrePoincare.ginibreLampertiCenterDrift","Measurable","Nat","Real","Real.measurableSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Field.toSemifield","GinibrePoincare.ginibreLampertiCenterDrift","GinibrePoincare.ginibreLampertiCenterDrift._proof_1","HDiv.hDiv","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","Measurable","Measurable.const_div","Measurable.const_mul","Measurable.fun_sub","Measurable.sqrt","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Real.sqrt","Semifield.toDivisionSemiring","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","id","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurableDiv_of_mul_inv","measurable_id'"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiPathFunctional","type_dependencies":["GinibrePoincare.Configuration","NNReal","Nat","Real"],"value_dependencies":["Filter.atTop","Filter.limUnder","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRiemannFunctional","NNReal","Nat","Nat.instPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instInhabited","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instNonemptyOfInhabited"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiPathFunctional_eq_integral","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous","DivInvMonoid.toDiv","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiPathFunctional","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.pairwiseRadius","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instDivInvMonoid","Real.instLT","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.sqrt","Real.toNNReal","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.instNormedAddCommGroup","ContDiff.continuous","Continuous","Continuous.comp","Continuous.continuousOn","ContinuousOn.comp_continuous","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","EMetricSpace.metrizableSpace","ENat","Eq.mp","Eq.refl","Filter","Filter.Tendsto","Filter.Tendsto.div_const","Filter.Tendsto.limUnder_eq","Filter.Tendsto.sub","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.ginibreLampertiRadialDrift_continuousOn","GinibrePoincare.ginibreLampertiRiemannFunctional","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibre_contDiff_pairwiseRadius","GinibrePoincare.itoContinuousScalarRiemann_fin_tendsto","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.instTopologicalSpace","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.sqrt","Real.toNNReal","Real.toNNReal_coe","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.Icc","Set.Ioi","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","congrFun'","continuous_real_toNNReal","funext","id","instAddNat","instArchimedeanNat","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSub","instInhabitedNat","instInnerProductSpaceRealComplex","instIsDirectedOrder","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instTopENat","intervalIntegral","nhds","tendsto_const_nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiPathFunctional_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiPathFunctional","Measurable","MeasurableSpace.pi","NNReal","Nat","Real","Real.measurableSpace"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.measurableSpace","Countable.LindelofSpace","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Filter.atTop","Filter.limUnder","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiPathFunctional","GinibrePoincare.ginibreLampertiRiemannFunctional","GinibrePoincare.ginibreLampertiRiemannFunctional_measurable","Measurable.stronglyMeasurable","MeasurableSpace.pi","MeasureTheory.StronglyMeasurable.limUnder","MeasureTheory.StronglyMeasurable.measurable","MetricSpace.toEMetricSpace","NNReal","Nat","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instPreorder","OrderTopology.of_linearLocallyFinite","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instCompleteSpace","Real.instInhabited","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","instCountableNat","instDiscreteTopologyNat","instIsCountablyGenerated_atTop","instNonemptyOfInhabited","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopologicalSpaceNat","measurable_pi_lambda"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiGenerator","name":"GinibrePoincare.ginibreLampertiRadialDrift","type_dependencies":["Nat","Real"],"value_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.ginibreLampertiRadialDrift._proof_1","GinibrePoincare.recenteredGammaShape","HDiv.hDiv","HMul.hMul","HSub.hSub","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.sqrt","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiGenerator","name":"GinibrePoincare.ginibreLampertiRadialDrift._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiGenerator","name":"GinibrePoincare.ginibreLampertiRadialDrift_continuousOn","type_dependencies":["ContinuousOn","GinibrePoincare.ginibreLampertiRadialDrift","Nat","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set.Ioi","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous.continuousAt","Continuous.mul","ContinuousAt.continuousWithinAt","ContinuousAt.div","ContinuousAt.sub","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Field.toSemifield","GinibrePoincare.ginibreLampertiRadialDrift._proof_1","GinibrePoincare.recenteredGammaShape","GroupWithZero.toDivInvMonoid","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mpr","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","LT.lt.ne'","Membership.mem","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","Pi.instDiv","Pi.instMul","Pi.instSub","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.continuous_sqrt","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.pseudoMetricSpace","Real.sqrt","Real.sqrt_pos","Semifield.toDivisionSemiring","Set","Set.Ioi","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_const","instHDiv","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiGenerator","name":"GinibrePoincare.ginibreLampertiRadialDrift_measurable","type_dependencies":["GinibrePoincare.ginibreLampertiRadialDrift","Measurable","Nat","Real","Real.measurableSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Field.toSemifield","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.ginibreLampertiRadialDrift._proof_1","GinibrePoincare.recenteredGammaShape","HDiv.hDiv","HMul.hMul","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","Measurable","Measurable.const_div","Measurable.const_mul","Measurable.fun_sub","Measurable.sqrt","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Real.sqrt","Semifield.toDivisionSemiring","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","id","instHDiv","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurableDiv_of_mul_inv","measurable_id'"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiRiemannFunctional","type_dependencies":["GinibrePoincare.Configuration","NNReal","Nat","Real"],"value_dependencies":["DivInvMonoid.toDiv","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.ginibreLampertiRiemannFunctional._proof_1","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","NNReal","NNReal.toReal","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.sqrt","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiRiemannFunctional._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiRiemannFunctional.eq_1","type_dependencies":["DivInvMonoid.toDiv","Eq","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.ginibreLampertiRiemannFunctional","GinibrePoincare.ginibreLampertiRiemannFunctional._proof_1","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","NNReal","NNReal.toReal","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.sqrt","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRiemannFunctional","NNReal","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","name":"GinibrePoincare.ginibreLampertiRiemannFunctional_measurable","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRiemannFunctional","Measurable","MeasurableSpace.pi","NNReal","Nat","Real","Real.measurableSpace"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff.continuous","Continuous.measurable","ContinuousAdd.measurableMul\u2082","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.measurable_sum","Finset.sum","Finset.univ","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ginibreLampertiRadialDrift","GinibrePoincare.ginibreLampertiRadialDrift_measurable","GinibrePoincare.ginibreLampertiRiemannFunctional._proof_1","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibre_contDiff_pairwiseRadius","GinibrePoincare.pairwiseRadius","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalRing.toIsSemitopologicalRing","Measurable","Measurable.comp","Measurable.div_const","Measurable.mul_const","Measurable.sub","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","NNReal","NNReal.toReal","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","OfNat.ofNat","One.toOfNat1","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.continuous_sqrt","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.sqrt","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","T5Space.toT1Space","T6Space.toT0Space","T6Space.toT5Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","Topolog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_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness","name":"GinibrePoincare.ginibreLangevinDrift_lipschitzOn_compact","type_dependencies":["Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","Exists","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","IsCompact","LipschitzOnWith","Membership.mem","MetricSpace.toEMetricSpace","NNReal","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","pseudoEMetricSpacePi"],"value_dependencies":["And","And.casesOn","And.intro","Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","Exists","Exists.casesOn","Exists.intro","Filter","Filter.instMembership","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_local_lipschitz","IsCompact","LipschitzOnWith","LocallyLipschitzOn.exists_lipschitzOnWith_of_compact","Membership.mem","MetricSpace.toEMetricSpace","NNReal","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","mem_nhdsWithin_of_mem_nhds","nhds","nhdsWithin","pseudoEMetricSpacePi","pseudoMetricSpacePi"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathDriftRegularity","name":"GinibrePoincare.ginibreLangevinDrift_local_integral_curve","type_dependencies":["AddCommMonoid.toAddMonoid","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Eq","Exists","Field.toSemifield","Fin","GT.gt","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instLT","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.normedField","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Set","Set.Ioo","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instContinuousSMulForall","instHAdd","instHSub","instInnerProductSpaceRealComplex","instPolynormableSpace"],"value_dependencies":["Complex","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt\u2080","ContDiffAt.of_le","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.trans","False","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_contDiffAt","InnerProductSpace.toNormedSpace","LE.le","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.complete","Pi.normedAddCommGroup","Pi.normedSpace","Preorder.toLE","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","True","True.intro","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","eq_false","eq_true","instInnerProductSpaceRealComplex","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathDriftRegularity","name":"GinibrePoincare.ginibreLangevinDrift_local_lipschitz","type_dependencies":["And","Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","Exists","Filter","Filter.instMembership","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","LipschitzOnWith","Membership.mem","MetricSpace.toEMetricSpace","NNReal","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","UniformSpace.toTopologicalSpace","nhds","pseudoEMetricSpacePi"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiffAt.exists_lipschitzOnWith","ContDiffAt.of_le","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.trans","False","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_contDiffAt","InnerProductSpace.toNormedSpace","LE.le","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.normedAddCommGroup","Pi.normedSpace","Preorder.toLE","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","True","True.intro","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","eq_false","eq_true","instInnerProductSpaceRealComplex","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUPath","name":"GinibrePoincare.ginibreLangevinDrift_one","type_dependencies":["Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instRCLike","Eq","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","HMul.hMul","HSMul.hSMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instMul","Real.instNatCast","Real.instNeg","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instCommCStarAlgebraComplex","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero.toDivisionCommMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.normSq","Complex.ofReal","Complex.ofReal_mul","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.instOfNat","Fin.instUnique","Fin.instUnique._proof_1","Fin.subsingleton_one","Finset","Finset.instSetLike","Finset.instSingleton","Finset.sum","Finset.sum_congr","Finset.sum_singleton","Finset.univ","Finset.univ_unique","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoulombInteraction","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift._proof_1","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toZeroHomClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instField","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instRing","Real.instZero","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toMonoid","SetLike.instMembership","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Subsingleton.elim","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","div_one","div_zero","eq_self","funext","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","map_zero","neg_smul","of_eq_true","one_pow","smul_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationDynamics","name":"GinibrePoincare.ginibreLangevinDrift_permute","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.permute","Nat","Real"],"value_dependencies":["Algebra.toSMul","Complex","Complex.instAdd","Complex.instNormedField","Complex.instRCLike","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreCoulombInteraction","GinibrePoincare.ginibreCoulombInteraction_permute","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.permute","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","congrArg","id","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianDrift","name":"GinibrePoincare.ginibreLangevinDrift_re_hamiltonian","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.realCoordinateDirection","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRi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paceRealComplex","instIsCancelMulZero","instLTNat","instMulZeroClassOfSemiring","instOfNat","instOfNatNat","instPreorderENat","instReflLe","instSMulOfMul","instTopENat","instZeroENat","mul_neg","mul_one","mul_sub","ne_of_gt","neg_mul","not_false_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakGradient","name":"GinibrePoincare.ginibreLebesgueDensityReal_ne_zero_ae","type_dependencies":["Complex","Complex.measurableSpace","Filter.Eventually","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Nat","Ne","OfNat.ofNat","Real","Real.instZero","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.measurableSpace","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_zero","Eq","Eq.trans","Field.toSemifield","Filter","Filter.instMembership","Filter.mp_mem","Filter.univ_mem'","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianWeight","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_absolutelyContinuous_complexGaussianMeasure","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeDensity_ne_zero_ae","GinibrePoincare.vandermondeWeight","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","LT.lt","LT.lt.ne'","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous.ae_le","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.cast_ne_zero","Nat.instPreorder","Ne","Neg.neg","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","OfNat.ofNat","Real","Real.exp","Real.exp_ne_zero","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.instZero","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pi","Real.pi_ne_zero","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Set","Set.instMembership","Set.ofPred","True","Zero.toOfNat0","congrArg","congrFun'","div_ne_zero","eq_self","id","instHDiv","instHMul","instHPow","instLTNat","instOfNatNat","isReduced_of_noZeroDivisors","mul_ne_zero","of_eq_true","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDistributionalGradient","name":"GinibrePoincare.ginibreLebesgueDensityReal_ne_zero_of_collisionFree","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","LT.lt","Nat","Ne","OfNat.ofNat","Real","Real.instZero","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instSemiring","Complex.instZero","Complex.normSq","Complex.normSq_eq_zero","DFunLike.coe","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianWeight","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermonde_ne_zero_iff","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mp","Iff.mpr","LT.lt","LT.lt.ne'","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Nat.cast_ne_zero","Nat.instPreorder","Ne","Neg.neg","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","OfNat.ofNat","Real","Real.exp","Real.exp_ne_zero","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.instZero","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pi","Real.pi_ne_zero","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Zero.toOfNat0","div_ne_zero","id","instHDiv","instHMul","instHPow","instLTNat","instMulZer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","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp_apply","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.ginibreLinearStatistic","GinibrePoincare.ginibreLinearStatistic_contDiff","GinibrePoincare.ginibreLinearStatistic_fderiv_direction","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat","Nat.cast_one","Nat.cast_zero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","fderiv","fderiv_comp","id","instAddMonoidWithOneENat","instCharZeroENat","instInnerProductSpaceRealComplex","instOneENat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreLinearStatisticDifferential","name":"GinibrePoincare.ginibreLinearStatistic_contDiff","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreLinearStatistic","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.comp","ContDiff.sum","ContinuousLinearMap.contDiff","ContinuousLinearMap.proj","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.univ","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreLinearStatisticDifferential","name":"GinibrePoincare.ginibreLinearStatistic_fderiv_direction","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateDirection","GinibrePoincare.ginibreLinearStatistic","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminorme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false","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreLinearStatisticDifferential","name":"GinibrePoincare.ginibreLinearStatistic_gradient_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","Field.toSemifield","GinibrePoincare.Configuration","GinibrePoincare.ginibreLinearStatistic","GinibrePoincare.realGradientNormSq","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LipschitzWith","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toNSMul","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.opNorm_comp_le","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.univ","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.Configuration","GinibrePoincare.complexRealDual_norm_sq","GinibrePoincare.coordinateDirection","GinibrePoincare.ginibreLinearStatistic","GinibrePoincare.ginibreLinearStatistic_chain_direction","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.realGradientNormSq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","LipschitzWith","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Co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attice.toSemilatticeInf","LinearOrder.toPartialOrder","LipschitzWith","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_ofNat","Mathlib.Tactic.FieldSimp.zpow'_one","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.const_mul","MeasureTheory.Integrable.mono'","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable_sq","MeasureTheory.MemLp.norm","MeasureTheory.MemLp.of_bound","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_const_mul","MeasureTheory.integral_map","MeasureTheory.integral_mono","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toSMulWithZero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_one","Nat.cast_pos'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Nat.instSemiring","Ne","NeZero.charZero_one","NeZero.one","Neg.neg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.instPow","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PiLp.continuous_toLp","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolishSpace.toSecondCountableTopology","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.le_sqrt",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.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityCFCompactExhaustion._proof_2","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SigmaCompactSpace","Subtype","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instProperSpace","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCF_locallyCompact","HereditarilyLindelof.to_Lindelof","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","SecondCountableTopology.toHereditarilyLindelof","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","TopologicalSpace.instSecondCountableTopologyForallOfCountable","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","instCountableFin","instHereditarilyLindelofSpaceSubtype","instPseudoEMetricSpaceSubtype","instTopologicalSpaceSubtype","pseudoEMetricSpacePi","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityCF_locallyCompact","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","LocallyCompactSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instProperSpace","Fin","Fin.fintype","Finite.of_fintype","Function.locallyCompactSpace_of_finite","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.isOpen_collisionFree","IsOpen.locallyCompactSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.ofPred","UniformSpace.toTopologicalSpace","locallyCompact_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityCompactSet","type_dependencies":["GinibrePoincare.Configuration","Nat","Set"],"value_dependencies":["CompactExhaustion","CompactExhaustion.instFunLikeNatSet","Complex","Complex.instNormedField","DFunLike.coe","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCFCompactExhaustion","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.image","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityCompactSet_isCompact","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCompactSet","IsCompact","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CompactExhaustion","CompactExhaustion.instFunLikeNatSet","CompactExhaustion.isCompact","Complex","Complex.instNormedField","DFunLike.coe","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCFCompactExhaustion","IsCompact.image","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMet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.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityProduct","name":"GinibrePoincare.ginibreLocalRegularityDirectional_compact","type_dependencies":["Complex","Complex.instZero","GinibrePoincare.ginibreLocalRegularityDirectional","HasCompactSupport","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","PseudoMetricSpace.toUniformSpace","Real","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instZero","DenselyNormedField.toNontriviallyNormedField","HasCompactSupport","HasCompactSupport.fderiv_apply","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityProduct","name":"GinibrePoincare.ginibreLocalRegularityDirectional_product","type_dependencies":["Complex","Complex.instAdd","Complex.instMul","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.ginibreLocalRegularityDirectional","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Pi.instMul","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Top.top","WithTop.some","instHAdd","instHMul","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.differentiableAt","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.trans","False","Field.toSemifield","GinibrePoincare.ginibreLocalRegularityDirectional","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","eq_self","fderiv","fderiv_mul","id","instDistribOfSemiring","instHAdd","instHMul",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Poincare.ginibreLocalRegularityDirectional_smooth","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.ginibreLocalRegularityDirectional","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","ContDiff.clm_apply","ContDiff.fderiv_right","DenselyNormedField.toNontriviallyNormedField","ENat","InnerProductSpace.toNormedSpace","LE.le","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Std.le_refl._simp_1","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","contDiff_const","fderiv","instInnerProductSpaceRealComplex","instPreorderENat","instReflLe","instTopENat","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityExhaustionCutoff","type_dependencies":["GinibrePoincare.Configuration","LT.lt","Nat","OfNat.ofNat","Real","instLTNat","instOfNatNat"],"value_dependencies":["And","Classical.choose","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCompactSet","GinibrePoincare.ginibreLocalRegularityExhaustionCutoff._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.instOne","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopENat","nhds","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityExhaustionCutoff._proof_1","type_dependencies":["And","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCompactSet","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.instOne","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopENat","nhds","tsupport"],"value_dependencies":["GinibrePoincare.ginibreLocalRegularityCompactSet","GinibrePoincare.ginibreLocalRegularityCompactSet_isCompact","GinibrePoincare.ginibreLocalRegularityCompactSet_subset","GinibrePoincare.ginibreLocalRegularity_exists_compact_interior_cutoff","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityExhaustionCutoff.congr_simp","type_dependencies":["Eq","GinibrePoincare.Configur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Like","Real.normedField","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","ContDiff.sum","DenselyNormedField.toNontriviallyNormedField","ENat","Finset","Finset.instSetLike","Finset.univ","Fintype","GinibrePoincare.ginibreLocalRegularityDirectional","GinibrePoincare.ginibreLocalRegularityDirectional_smooth","InnerProductSpace.toNormedSpace","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SetLike.instMembership","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityOpenSet","type_dependencies":["GinibrePoincare.Configuration","Nat","Set"],"value_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCompactSet","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","interior"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityOpenSet_contains_compact","type_dependencies":["Complex","Complex.instNormedField","Exists","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityOpenSet","IsCompact","LE.le","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.ofPred","UniformSpace.toTopologicalSpace"],"value_dependencies":["ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.instNormedField","Eq","Eq.mpr","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityOpenSet","GinibrePoincare.ginibreLocalRegularityOpenSet_iUnion","GinibrePoincare.ginibreLocalRegularityOpenSet_isOpen","GinibrePoincare.ginibreLocalRegularityOpenSet_monotone","IsCompact","IsCompact.elim_directed_cover","LE.le","Membership.mem","Monotone.directed_le","Nat","Nat.instCommSemiring","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PartialOrder.toPreorder","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","StarOrderedRing.toIsOrderedRing","UniformSpace.toTopologicalSpace","congrArg","id","instArchimedeanNat","instInhabitedNat","instIsDirectedOrder","instNonemptyOfInhabited"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","name":"GinibrePoincare.ginibreLocalRegularityOpenSet_iUnion","type_dependencies":["Eq","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityOpenSet","Nat","Set","Set.iUnion","Set.ofPred"],"value_dependencies":["And","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompactExhaustion","CompactExhaustion.exists_mem","CompactExhaustion.instFunLikeNatSet","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.instNormedField","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreLocalRegularityCFCompactExhaustion","GinibrePoincare.ginibreLocalRegularityCompactSet","GinibrePoincare.ginibreLocalRegularityCompactSet_subset","GinibrePoincare.ginibreLocalRegularityCompactSet_subset_open_succ","GinibrePoincare.ginibreLocalRegularityOpenSet","GinibrePoincare.ginibreLocalRegularityOpenSet_subset_compact","HAdd.hAdd","Iff.mpr","LE.le.trans","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Subset.antisymm","Set.iUnion","Set.iUnion_subset","Set.instCompleteAtomicBooleanAlgebra","Set.instMembership","Set.mem_iUnion","Set.ofPred","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpac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CommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.ofReal","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instMul","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.some","WithTop.zero","Zero.toOfNat0","autoParam","congr","congrArg","congrFun'","contDiff_const","fderiv","funext","id","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instPreorderENat","instReflLe","instTopENat","instZeroENat","mul_comm","not_false_eq_true","of_eq_true","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConfigurationCutoff","name":"GinibrePoincare.ginibreLocalRegularity_configuration_cutoff_exists_weak_derivatives","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Exists","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasurableSet","MeasurableSpace.pi","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instFintypeProd","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopENat","measureSpaceOfInnerProductSpace","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClas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","Semiring.toNonAssocSemiring","Set","Set.image","Set.preimage","Set.preimage_image_eq","Top.top","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","Zero.toOfNat0","autoParam","cast","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instCountableFin","instCountableProd","instDistribOfSemiring","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace","one_smul","secondCountable_of_proper","smul_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinates","name":"GinibrePoincare.ginibreLocalRegularity_coordinate_volume","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","And","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instSMulNNRealOfMulAction","Eq","EquivLike.toFunLike","EuclideanSpace","Exists","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.map","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Monoid.toMulAction","NNReal","NNReal.instPartialOrder","NNReal.instZero","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.topologicalSpace","Preorder.toLT","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instAddCommGroup","Real.instDivisionRing","Real.instRCLike","Real.instRing","Real.measurableSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCountableFin","instCountableProd","instFintypeProd","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","Algebra.id","And","And.intro","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","ContinuousAdd.measurableAdd","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.isAddHaarMeasure_map","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instSMulNNRealOfMulAction","Eq","EquivLike.toFunLike","EuclideanSpace","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.proper_real","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","HSMul.h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.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.memLp","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","Preorder.toLT","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivisionRing","Real.instMonoid","Real.instRCLike","Real.instRing","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","fact_one_le_two_ennreal","fderiv","funext","id","instCountableFin","instCountableProd","instFintypeProd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSecondCountableTopologyReal","instTopENat","instZeroENat","measureSpaceOfInnerProductSpace","not_false_eq_true","of_eq_true","smul_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityInterior","name":"GinibrePoincare.ginibreLocalRegularity_cutoff_weak_derivative_interior","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instMul","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instZero","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Field.toSemifield","FiniteDimensional","HMul.hMul","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureT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HaarMeasure.instHasTemperateGrowth","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.integral_neg","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instAddGroup","Real.instDivisionRing","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.normedField","RingHom.id","SMulZeroClass.toSMul","SchwartzMap","SchwartzMap.instAddCommGroup","SchwartzMap.instFunLike","SchwartzMap.instIsNegApply","SchwartzMap.instLineDeriv","SchwartzMap.instModule","SchwartzMap.instNeg","SchwartzMap.instTopologicalSpace","SchwartzMap.neg_apply","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set","Set.Elem","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","TemperedDistribution","TemperedDistribution.MemSobolev","TemperedDistribution.MemSobolev.congr_simp","TemperedDistribution.MemSobolev.lineDerivOp","TemperedDistribution._proof_1","TemperedDistribution.instLaplacian","TemperedDistribution.instLineDeriv","TemperedDistribution.memSobolev_zero_iff","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformConvergenceCLM.instAddCommGroup","UniformConvergenceCLM.instFunLike","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congr","congrArg","congrFun'","fact_one_le_two_ennreal","fderiv","funext","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instTopENat","measureSpaceOfInnerProductSpace","neg_mul","rfl","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactTests","name":"GinibrePoincare.ginibreLocalRegularity_exists_compact_cutoff","type_dependencies":["And","BorelSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Exists","Filter.EventuallyEq","FiniteDimensional","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","IsCompact","MeasurableSpace","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instOne","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instTopENat","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.casesOn","And.intro","BorelSpace","Bornology.IsBounded.exists_pos_norm_le","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiffBump","ContDiffBump.contDiff","ContDiffBump.eventuallyEq_one_of_mem_ball","ContDiffBump.hasCompactSupport","ContDiffBump.mk","ContDiffBump.rIn","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Filter.EventuallyEq","FiniteDimensional","GT.gt","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","InnerProductSpace","Inner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oidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.comp","ContDiff.mul","Continuous.continuousAt","ContinuousLinearEquiv","ContinuousLinearEquiv.contDiff","ContinuousLinearEquiv.continuous","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.toHomeomorph","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.comp_tendsto","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanEquiv","GinibrePoincare.exists_ginibreInteriorCutoff","GinibrePoincare.ginibreLocalRegularity_exists_compact_cutoff","HMul.hMul","HasCompactSupport","HasCompactSupport.comp_homeomorph","HasCompactSupport.mul_right","InnerProductSpace.toNormedSpace","IsCompact","IsCompact.image","LE.le","LE.le.trans","LT.lt","MeasurableSpace.pi","Membership.mem","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.instMul","Pi.instOne","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivisionRing","Real.instMul","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.image","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop.some","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCountableFin","instCountableProd","instFintypeProd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instTopENat","mul_one","nhds","of_eq_true","rfl","tsupport","tsupport_mul_subset_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConvolution","name":"GinibrePoincare.ginibreLocalRegularity_fderiv_convolution_kernel","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure","MeasureTheory.Measure.IsAddLeftInvariant","MeasureTheory.Measure.IsNegInvariant","MeasureTheory.SFinite","MeasureTheory.convolution","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","BorelSpace","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.continuous_fderiv","ContDiff.of_le","ContinuousAdd.measurableAdd","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.integral_apply","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.precompL","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.topologicalSpace","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.trans","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.convolutionExists_left","HasCompactSupport.fderiv","HasCompactSupport.hasFDerivAt_convolution_left","HasFDerivAt","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalAddGroup.toContinuousNeg","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","MeasurableSpace","MeasureTheory.ConvolutionExistsAt.integrable_swap","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure","MeasureTheory.Measure.IsAddLeftInvariant","MeasureTheory.Measure.IsNegInvariant","MeasureTheory.SFinite","MeasureTheory.convolution","MeasureTheory.convolution_eq_swap","MeasureTheory.convolution_lsmul_swap","MeasureTheory.integral","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","MulZeroClass.toZero","Ne","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","PolynormableSpace.continuousSMul","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.isScalarTower","Real.me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Norm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTopENat","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","BorelSpace","BorelSpace.opensMeasurable","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.not_not","Classical.propDecidable","CommSemiring.toSemiring","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","False.elim","Field.toSemifield","Filter.Eventually","Filter.Eventually.mono","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional","GinibrePoincare.ginibreLocalRegularity_local_weak_derivative_unique","HMul.hMul","HasCompactSupport","Iff.mpr","InnerProductSpace.toNormedSpace","IsCompact","IsCompact.measurableSet","IsOpen","IsOpen.measurableSet","LE.le","LE.le.trans","Measurable","Measurable.find","Measurable.indicator","MeasurableSet","MeasurableSet.compl","MeasurableSet.union","MeasureTheory.AEStronglyMeasurable.ae_eq_mk","MeasureTheory.AEStronglyMeasurable.measurable_mk","MeasureTheory.AEStronglyMeasurable.mk","MeasureTheory.IsLocallyFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.ae_eq","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.MemLp.restrict","MeasureTheory.ae","MeasureTheory.ae_all_iff","MeasureTheory.ae_of_all","MeasureTheory.ae_restrict_mem","MeasureTheory.ae_restrict_of_ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","Monotone","MulZeroClass.toZero","MulZeroClass.zero_mul","Nat","Nat.decLe","Nat.find","Nat.find_min'","Nat.find_spec","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","Or","Or.inl","Or.inr","Or.resolve_right","PartialOrder.toPreorder","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivisionRing","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.indicator","Set.indicator_of_mem","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_self","fderiv","id","image_eq_zero_of_notMem_tsupport","instCountableNat","instHMul","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","of_eq_true","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealIndicator","name":"GinibrePoincare.ginibreLocalRegularity_indicator_real_equation","type_dependencies":["AddCommGroup.toAddCommMonoid","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Finset.sum","Finset.univ","Fintype","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.to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Theory.LocallyIntegrableOn","MeasureTheory.LocallyIntegrableOn.integrableOn_compact_subset","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integrable_indicator_iff","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.mul_zero","MulZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","NormedSpace","Not","OfNat.ofNat","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instLE","Set.instMembership","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","Zero","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_self","id","image_eq_zero_of_notMem_tsupport","instHMul","instHSMul","instMulZeroClassOfSemiring","isClosed_tsupport","of_eq_true","propext","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityWeakUniqueness","name":"GinibrePoincare.ginibreLocalRegularity_local_weak_derivative_unique","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Field.toSemifield","Filter.Eventually","FiniteDimensional","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","IsOpen","LE.le","MeasureTheory.IsLocallyFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivisionRing","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTopENat","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.continuous","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","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","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const_mul","MeasureTheory.integral_finsetSum","MeasureTheory.integral_sub","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Pi.instMul","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","Trans.trans","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalization.0.GinibrePoincare.ginibreLocalRegularity_localize_elliptic_equation._simp_1_1","congr","congrArg","fderiv","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instTransEq","mul_add","rfl","sub_mul","tsupport","tsupport_mul_subset_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalizedData","name":"GinibrePoincare.ginibreLocalRegularity_localized_elliptic_exists_weak_derivatives","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Exists","Field.toSemifield","FiniteDimensional","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreLocalRegularityDirectional","GinibrePoincare.ginibreLocalRegularityLaplacian","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","PseudoMetricSpace.toUniformSpace","Real","Real.de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inormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrthonormalBasis","OrthonormalBasis.instFunLike","Pi.instAdd","Pi.instSub","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedField","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instLE","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalizedData.0.GinibrePoincare.compact_sum","autoParam","congrArg","congrFun'","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_comm","rfl","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityMollifiedEquation","name":"GinibrePoincare.ginibreLocalRegularity_mollified_elliptic_equation","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure","MeasureTheory.Measure.IsAddLeftInvariant","MeasureTheory.Measure.IsNegInvariant","MeasureTheory.SFinite","MeasureTheory.convolution","MeasureTheory.integral","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHAdd","instHMul","instHSub","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.clm_apply","ContDiff.comp","ContDiff.continuous","ContDiff.fderiv_right","ContDiff.sub","Continuous.comp","Continuous.sub","ContinuousAdd.measurableAdd","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENat","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.sum_neg_distrib","Finset.univ","Fintype","Function.comp","GinibrePoincare.ginibreLocalRegularity_fderiv_convolution_kernel","GinibrePoincare.ginibreLocalRegularity_reflected_fderiv","GinibrePoincare.ginibreLocalRegularity_reflected_second","GinibrePoincare.ginibreLocalRegularity_second_convolution_kernel","HAdd","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_homeomorph","HasCompactSupport.fderiv_apply","HasDistribNeg.toInvolutiveNeg","Homeomorph.subLeft","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","IsScalarTower.right","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalAddGroup.toContinuousNeg","IsTopologicalAddGroup.to_continuousSub","LE.le","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport","MeasureTheory.Measure","MeasureTheory.Measure.IsAddLeftInvariant","MeasureTheory.Measure.IsNegInvariant","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.SFinite","MeasureTheory.ae_of_all","MeasureTheory.convolution","MeasureTheory.convolution_lsmul_swap","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_finset_sum","MeasureTheory.integral_neg","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toRing","NormedSpace","NormedSpace.toModule","Pi.instSub","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","congr","congrArg","congrFun'","contDiff_const","contDiff_id","continuous_const","continuous_id","eq_of_heq","fderiv","funext","id","instHAdd","instHMul","instHSMul","instHSub","instPreorderENat","instReflLe","instSeparatelyContinuousAddOfContinuousAdd","instTopENat","mul_comm","mul_neg","of_eq_true","rfl","sub_neg_eq_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealTests","name":"GinibrePoincare.ginibreLocalRegularity_real_tests_complex_equation","type_dependencies":["AddCommGroup.toAddCommMonoid","BorelSpace","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreLocalRegularityDirectional","GinibrePoincare.ginibreLocalRegularityLaplacian","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","BorelSpace","BorelSpace.opensMeasurable","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.addGroupWithOne","Complex.ext","Complex.imCLM","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.ofReal","Complex.ofRealCLM","Complex.reCLM","ContDiff","ContDiff.comp","ContDiff.continuous","Continuous","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.integrableAtFilter_comp","ContinuousLinearMap.integral_comp_comm","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","EMetricSpace.metrizableSpace","ENat","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Fintype","Function.comp","GinibrePoincare.ginibreLocalRegularityDirectional","GinibrePoincare.ginibreLocalRegularityDirectional_compact","GinibrePoincare.ginibreLocalRegularityDirectional_smooth","GinibrePoincare.ginibreLocalRegularityLaplacian","GinibrePoincare.ginibreLocalRegularityLaplacian_compact","GinibrePoincare.ginibreLocalRegularityLaplacian_smooth","HEq","HEq.refl","HMul.hMul","HSMul.hSMul","HSub","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","LE.le","LE.le.trans","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instMul","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomIsometric.ids","Semifield.toCommSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop.some","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealTests.0.GinibrePoincare.derivative_component","congr","congrArg","congrFun'","eq_of_heq","eq_self","fderiv","funext","id","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instSMulOfMul","instTopENat","map_smul","map_sub","map_sum","map_zero","nhds","of_eq_true","rfl","tsupport","tsupport_comp_subset"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConvolution","name":"GinibrePoincare.ginibreLocalRegularity_reflected_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","Neg.neg","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHSub","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp.congr_simp","ContinuousLinearMap.comp_id","ContinuousLinearMap.comp_neg","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.neg","ContinuousLinearMap.ring","ContinuousLinearMap.sub","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Function.comp","HSub.hSub","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","HasFDerivAt.sub","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MeasurableSpace","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instNeg","Real.instRCLike","Real.instRing","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","eq_self","fderiv","hasFDerivAt_const","hasFDerivAt_id","id","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instPolynormableSpace","instTopENat","instZeroENat","neg_apply","not_false_eq_true","of_eq_true","zero_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConvolution","name":"GinibrePoincare.ginibreLocalRegularity_reflected_second","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","BorelSpace","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHSub","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","BorelSpace","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.clm_apply","ContDiff.fderiv_right","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.neg","ContinuousLinearMap.neg_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivisionRing.toRing","ENat","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.ginibreLocalRegularity_reflected_fderiv","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","LE.le","MeasurableSpace","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace","NormedSpace.toModule","Pi.instNeg","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instNeg","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Std.le_refl._simp_1","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","congrArg","congrFun'","contDiff_const","fderiv","fderiv_neg","funext","id","instHSub","instPreorderENat","instReflLe","instTopENat","neg_neg","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRestrictedData","name":"GinibrePoincare.ginibreLocalRegularity_restricted_elliptic_exists_weak_derivatives","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","BorelSpace","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Exists","Field.toSemifield","FiniteDimensional","Finset.sum","Finset.univ","Fintype","GinibrePoincare.ginibreLocalRegularityDirectional","GinibrePoincare.ginibreLocalRegularityLaplacian","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","MeasurableSet","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","M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tractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.some","congrArg","contDiff_const","fderiv","funext","id","instPreorderENat","instReflLe","instTopENat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityTemperedEquation","name":"GinibrePoincare.ginibreLocalRegularity_toLp_tempered_apply","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","Complex","Complex.instCompleteSpace","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Finite","FiniteDimensional","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Lp.toTemperedDistribution","MeasureTheory.Measure.IsAddHaarMeasure.instHasTemperateGrowth","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","MeasureTheory.integral","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","RingHom.id","SchwartzMap","SchwartzMap.instAddCommGroup","SchwartzMap.instFunLike","SchwartzMap.instModule","SchwartzMap.instTopologicalSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.ofPred","TemperedDistribution","TemperedDistribution._proof_1","UniformConvergenceCLM.instFunLike","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","Complex","Complex.instCompleteSpace","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousENorm.toENorm","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Filter.mp_mem","Filter.univ_mem'","Finite","FiniteDimensional","HMul.hMul","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.toTemperedDistribution","MeasureTheory.Lp.toTemperedDistribution_apply","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.instHasTemperateGrowth","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","RingHom.id","SMulZeroClass.toSMul","SchwartzMap","SchwartzMap.instAddCommGroup","SchwartzMap.instFunLike","SchwartzMap.instModule","SchwartzMap.instTopologicalSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiri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roup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fact_one_le_two_ennreal","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","measureSpaceOfInnerProductSpace","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","Classical.propDecidable","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff","Continuous.aestronglyMeasurable","Continuous.bounded_above_of_compact_support","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","ContinuousLinearMap.zero_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mp","Eq.mpr","Eq.trans","EuclideanSpace","Exists","Exists.casesOn","Field.toSemifield","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.compactSupport_ginibreEuclideanGradient","GinibrePoincare.continuous_ginibreEuclideanGradient","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_coordinate","GinibrePoincare.ginibreLocalWeak_compact_gradient_memLp","GinibrePoincare.ginibreMeasure","HMul.hMul","HasCompactSupport","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","LT.lt","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable.inner","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.ae_eq","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.MemLp.of_le_mul","MeasureTheory.ae","MeasureTheory.ae_of_all","Membership.mem","MetricSpace.toEMetricSpace","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNorm","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PiLp.ext","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","PiLp.secondCountableTopology","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Preorder.toLE","Prod","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnital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mmMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommMonoidWithZero.toMonoidWithZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","EuclideanDomain.toMulDivCancelClass","Field.toEuclideanDomain","Field.toSemifield","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.instCommMonoid","Fin.instNeZeroHAddNatOfNat_mathlib_1","Fin.instNonUnitalCommRing","Fin.instOfNat","Fin.sum_univ_two","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_div","Finset.univ","Fintype.sum_prod_type","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreCoordinateDirection._proof_1","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreLebesgueDensityReal_mul_pregenerator_eq_divergence","GinibrePoincare.ginibreLebesgueDensityReal_ne_zero_ae","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibre_ae_collisionFree","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommMonoidWithZero","Real.instDivInvMonoid","Real.instField","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingGreen.0.GinibrePoincare.ginibreLocalWeak_generator_divergence_ae._simp_1_1","congr","congrArg","congrFun'","eq_of_heq","eq_self","fderiv","funext","id","instCommCStarAlgebraComplex","instDecidableEqFin","instDistribOfSemiring","instFintypeProd","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","instTopENat","ite","ite_congr","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","mul_div_assoc","mul_div_cancel_left\u2080","of_eq_true","one_div","one_ne_zero._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingGreen","name":"GinibrePoincare.ginibreLocalWeak_generator_green","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat"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ero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PiLp.ext","PiLp.innerProductSpace._proof_1","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.ofLp","Zero.toOfNat0","closure_minimal","congrArg","congrFun'","eq_self","fderiv","fderiv_of_notMem_tsupport","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","isClosed_tsupport","of_eq_true","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingContinuity","name":"GinibrePoincare.ginibreLocalWeak_pairing_limit","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","Inner.inner","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.congr'","Filter.Tendsto.fst_nhds","Filter.Tendsto.inner","Filter.Tendsto.mul","Filter.Tendsto.snd_nhds","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instMul","Real.instRCLike","Real.metricSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","Subtype","TopologicalSpace.t2Space_of_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Poincare.ginibreMeasure","GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure._proof_1","GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure._proof_4","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure","name":"GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure","name":"GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_mass","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure","GinibrePoincare.ginibreSymmetricL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",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oidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.integral","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMul","Real.instNeg","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.re","Continuous.aestronglyMeasurable","Continuous.const_mul","Continuous.rexp","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DivisionRing.toRing","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullEvolution","GinibrePoincare.ginibreGeneratorVectorSpectralMeasure","GinibrePoincare.ginibreGeneratorVectorSpectralMeasure_semigroup","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure","GinibrePoincare.ginibreSymmetricL2","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Measurable.aemeasurable","MeasurableNeg.measurable_neg","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEStronglyMeasurable","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","M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oMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Ici","Set.Iic","Set.ext","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.instUnion","Set.preimage","SetLike.instMembership","Singleton.singleton","StandardBorelSpace.instMeasurableEq","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","Union.union","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_1","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_2","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_3","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_4","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_5","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_6","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure.0.GinibrePoincare.ginibreNegativeGeneratorVectorSpectralMeasure_support._simp_1_7","congr","congrArg","id","iff_self","inferInstance","instClosedIciTopology","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsTopologicalRingReal","instLTNat","instMeasurableSingletonClassOfMeasurableEq","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","le_of_not_gt","measurableSet_Ici","of_eq_true","propext","rfl","standardBorel_of_polish"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","name":"GinibrePoincare.ginibreNegativeTest","type_dependencies":["Real"],"value_dependencies":["Neg.neg","Real","Real.instNeg","Real.smoothTransition"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","name":"GinibrePoincare.ginibreNegativeTest.eq_1","type_dependencies":["Eq","GinibrePoincare.ginibreNegativeTest","Neg.neg","Real","Real.instNeg","Real.smoothTransition"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreNegativeTest","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","name":"GinibrePoincare.ginibreNegativeTest_antitone","type_dependencies":["Antitone","GinibrePoincare.ginibreNegativeTest","Real","Real.instPreorder"],"value_dependencies":["LE.le","Monotone.comp_antitone","Neg.neg","Preorder.toLE","Real","Real.instAddCommGroup","Real.instIsOrderedAddMonoid","Real.instNeg","Real.instPreorder","Real.partialOrder","Real.smoothTransition","Real.smoothTransition.monotone","neg_le_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","name":"GinibrePoincare.ginibreNegativeTest_deriv_nonpos","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","GinibrePoincare.ginibreNegativeTest","LE.le","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instZero","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv"],"value_dependencies":["Antitone.deriv_nonpos","DenselyNormedField.toNontriviallyNormedField","GinibrePoincare.ginibreNegativeTest","GinibrePoincare.ginibreNegativeTest_antitone","Real","Real.denselyNormedField","Real.instIsStrictOrderedRing","Real.linearOrder","instOrderTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","name":"GinibrePoincare.ginibreNegativeTest_lipschitz","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","Exists","GinibrePoincare.ginibreNegativeTest","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","Real","Real.metricSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZe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mp","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUBrownianClock_coe","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","Mul","MulZeroClass.toZero","NNReal","NNReal.coe_le_coe","NNReal.coe_nonneg","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.exp","Real.exp_le_exp","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUInnovation","name":"GinibrePoincare.ginibreOUBrownianClock_monotone","type_dependencies":["GinibrePoincare.ginibreOUBrownianClock","Monotone","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder"],"value_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","CommSemiring.toNonUnitalCommSemiring","Distrib.toAdd","Eq.mp","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUBrownianClock_mono","HAdd.hAdd","HSub.hSub","LE.le","NNReal","NNReal.addLeftMono","NNReal.instCommSemiring","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instStarOrderedRing","NNReal.instSub","NonUnitalCommSemiring.toNonUnitalSemiring","PartialOrder.toPreorder","Preorder.toLE","Semiring.toAddCommMonoid","StarOrderedRing.toExistsAddOfLE","add_tsub_cancel_of_le","congrArg","instDistribOfSemiring","instHAdd","instHSub","instStarRingNNReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUTimeChange","name":"GinibrePoincare.ginibreOUBrownianClock_variance","type_dependencies":["CommRing.toNonUnitalCommRing","Distrib.toMul","Eq","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","HMul.hMul","HPow.hPow","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","Monoid.toNPow","NNReal","NNReal.instSemiring","NNReal.mk","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","Real","Real.commRing","Real.instAddCommMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instPreorder","Real.instStarOrderedRing","Real.linearOrder","Real.partialOrder","Real.semiring","Semiring.toMonoid","StarOrderedRing.toExistsAddOfLE","instDistribOfSemiring","instHMul","instHPow","instOfNatNat","instStarRingReal","sq_nonneg"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUBrownianClock_coe","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance_coe","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.pow_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Ta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","GinibrePoincare.ginibreBrownianOURiemannSum","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_le_end","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.instPreorder","Nat.le_of_lt","Nat.succ_le_of_lt","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instInhabited","Real.instMul","Real.instSub","Real.pseudoMetricSpace","SetLike.instMembership","TopologicalSpace","UniformSpace.toTopologicalSpace","congrArg","funext","id","instAddNat","instHAdd","instHMul","instHSub","instNonemptyOfInhabited","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUFunctional","name":"GinibrePoincare.ginibreOUConvolutionFunctional_measurable","type_dependencies":["GinibrePoincare.ginibreOUConvolutionFunctional","Measurable","MeasurableSpace.pi","NNReal","Real","Real.measurableSpace"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","ContinuousAdd.measurableMul\u2082","ContinuousMul.measurableMul","ContinuousSub.measurableSub\u2082","Countable.LindelofSpace","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Filter.atTop","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.measurable_sum","Finset.univ","GinibrePoincare.ginibreBrownianOURiemannSum","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUStochasticWeight","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HMul.hMul","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","Measurable","Measurable.const_mul","Measurable.fun_sub","Measurable.stronglyMeasurable","MeasurableSpace.pi","MeasureTheory.StronglyMeasurable.limUnder","MeasureTheory.StronglyMeasurable.measurable","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","OrderTopology.of_linearLocallyFinite","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instInhabited","Real.instMul","Real.instSub","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","SetLike.instMembership","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","UniformSpace.toTopologicalSpace","id","instAddNat","instCountableNat","instDiscreteTopologyNat","instHAdd","instHMul","instHSub","instIsCountablyGenerated_atTop","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instNonemptyOfInhabited","instOfNatNat","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instTopologicalSpaceNat","measurable_pi_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUDecay","type_dependencies":["NNReal","Real"],"value_dependencies":["HMul.hMul","NNReal","NNReal.toReal","Neg.neg","Real","Real.exp","Real.instMul","Real.instNeg","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUDecay.eq_1","type_dependencies":["Eq","GinibrePoincare.ginibreOUDecay","HMul.hMul","NNReal","NNReal.toReal","Neg.neg","Real","Real.exp","Real.instMul","Real.instNeg","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreOUDecay","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUDecay_add","type_dependencies":["Distrib.toAdd","Eq","GinibrePoincare.ginibreOUDecay","HAdd.hAdd","HMul.hMul","NNReal","NNReal.instSemiring","Real","Real.instMul","instDistribOfSemiring","instHAdd","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","GinibrePoincare.ginibreOUDecay","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.negOfNat","Int.ofNat","Int.ra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brePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreInteractionCorrectedNoise","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["Algebra.toSMul","And","And.intro","And.left","And.right","CommCStarAlgebra.toNormedCommRing","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","ContDiffAt.continuousAt","ContinuousAt.comp_continuousWithinAt","ContinuousOn","ContinuousOn.intervalIntegrable","ContinuousOn.mono","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.coe_lt_coe","ENNReal.instCompleteLinearOrder","ENNReal.instLE","ENNReal.instPartialOrder","ENNReal.ofNNReal","ENat","Eq","Eq.mpr","Exists.intro","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.GinibreDrivenSegment","GinibrePoincare.ginibreDrivenHorizons","GinibrePoincare.ginibreDrivenMaximalLifetime","GinibrePoincare.ginibreDrivenMaximalValue","GinibrePoincare.ginibreDrivenMaximalValue_eq_segment","GinibrePoincare.ginibreInteractionCorrectedNoise","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreLangevinDrift_contDiffAt","GinibrePoincare.ginibreOUPath_corrected_original_volterra","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","Iff.mpr","InnerProductSpace.toNormedSpace","IntervalIntegrable","LE.le","LT.lt","LT.lt.le","LT.lt.trans_le","Lattice.toSemilatticeInf","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedAddGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.locallyFinite_volume","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Set","Set.Elem","Set.Icc","Set.Icc_subset_Icc_right","Set.instMembership","Set.uIcc","Set.uIcc_of_le","Subtype.mk","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopENat","intervalIntegral","le_iSup_of_le","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltVolterra","name":"GinibrePoincare.ginibreOUPath_corrected_original_volterra","type_dependencies":["Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","ContinuousOn","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","Fin.fint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l.pseudoMetricSpace","Real.toNNReal","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["ContinuousMap","Eq.refl","GinibrePoincare.ginibreOURealHorizonToNNReal","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianConfigurationOUReference","name":"GinibrePoincare.ginibreOURealHorizonToNNReal_reverse","type_dependencies":["ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","GinibrePoincare.ginibreHamiltonianCompactReverseTime","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.ginibreOURealHorizonToNNReal","LE.le","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.property","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instTopologicalSpaceSubtype"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","And.left","And.right","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Eq.mp","Eq.mpr","Eq.refl","GinibrePoincare.ginibreHamiltonianCompactReverseTime","GinibrePoincare.ginibreOUHorizonReverseTime","GinibrePoincare.ginibreOURealHorizonToNNReal","HSub.hSub","Iff.mpr","IsOrderedAddMonoid.toAddRightMono","LE.le","Membership.mem","NNReal","NNReal.coe_sub","NNReal.eq","NNReal.instPartialOrder","NNReal.instSub","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.coe_toNNReal","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLE","Real.instPreorder","Real.instSub","Real.instZero","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_coe","Real.toNNReal_le_toNNReal","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Subtype.ext","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instHSub","instTopologicalSpaceSubtype","sub_nonneg"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticOUWeight","name":"GinibrePoincare.ginibreOUStochasticWeight","type_dependencies":["NNReal","Real"],"value_dependencies":["HMul.hMul","HSub.hSub","NNReal","NNReal.toReal","Neg.neg","Real","Real.exp","Real.instMul","Real.instNeg","Real.instSub","Real.sqrt","instHMul","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUWeight","name":"GinibrePoincare.ginibreOUStochasticWeight.eq_1","type_dependencies":["Eq","GinibrePoincare.ginibreOUStochasticWeight","HMul.hMul","HSub.hSub","NNReal","NNReal.toReal","Neg.neg","Real","Real.exp","Real.instMul","Real.instNeg","Real.instSub","Real.sqrt","instHMul","instHSub"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreOUStochasticWeight","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUWeight","name":"GinibrePoincare.ginibreOUStochasticWeight_hasDerivAt","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.ginibreOUStochasticWeight","HMul.hMul","HasDerivAt","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Module.toDistribMulAction","NNReal","NNReal.toReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instHMul","instIsTopologicalRingReal"],"value_dependencies":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ield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreGaussian_affine_product_map","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUTransition_lintegral_noise","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance_coe","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.const_mul","Measurable.fst","Measurable.fun_add","Measurable.snd","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instRegularOfBorelSpaceOfR1SpaceOfIsFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.bind","MeasureTheory.Measure.ext_of_lintegral","MeasureTheory.Measure.lintegral_bind","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.lintegral","MeasureTheory.lintegral_map","MeasureTheory.lintegral_prod","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NNRat.rawCast","NNReal","NNReal.instDiv","NNReal.instOne","NNReal.instSemiring","NNReal.mk","NNReal.toReal","NPow.toPow","Nat","Nat.cast_one","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.aemeasurable","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Rat.rawCast","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instCompleteSpace",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bership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","id","instHAdd","instHMul","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUIndependent","name":"GinibrePoincare.ginibreOUValueFunctional_measurable","type_dependencies":["GinibrePoincare.ginibreOUValueFunctional","Measurable","MeasurableSpace.pi","NNReal","Real","Real.measurableSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd.measurableMul\u2082","GinibrePoincare.ginibreOUConvolutionFunctional","GinibrePoincare.ginibreOUConvolutionFunctional_measurable","GinibrePoincare.ginibreOUDecay","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Measurable.add","MeasurableSpace.pi","NNReal","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.instAdd","Real.instMul","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instIsTopologicalRingReal","instSecondCountableTopologyReal","measurable_const"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUVariance","type_dependencies":["NNReal"],"value_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance._proof_1","HDiv.hDiv","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instSub","Real.toNNReal","instHDiv","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUVariance._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUVariance.eq_1","type_dependencies":["DivInvMonoid.toDiv","Eq","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance._proof_1","HDiv.hDiv","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instSub","Real.toNNReal","instHDiv","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreOUVariance","NNReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreOUTransition","name":"GinibrePoincare.ginibreOUVariance_add","type_dependencies":["Distrib.toAdd","Eq","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUVariance","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid.toNPow","NNReal","NNReal.instSemiring","NNReal.toReal","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instAdd","Real.instMonoid","Real.instMul","instDistribOfSemiring","instHAdd","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUDecay_add","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreOUVariance_coe","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.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.ginibreOneParticleBrownianPath","GinibrePoincare.ginibreOneParticleCIRTransition","GinibrePoincare.ginibreOneParticleRadius","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","NNReal","NNReal.toReal","Nat","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Real","Real.measurableSpace","instOfNatNat"],"value_dependencies":["Eq","Eq.mpr","Eq.symm","GinibrePoincare.Configuration","GinibrePoincare.ginibreOneParticleBrownianPath","GinibrePoincare.ginibreOneParticleBrownianPath_radius_hasLaw","GinibrePoincare.ginibreOneParticleCIRTransition","GinibrePoincare.ginibreOneParticleRadius","GinibrePoincare.ginibreOneParticleRadiusTransition","GinibrePoincare.ginibreOneParticleRadiusTransition_eq_CIR","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","NNReal","NNReal.toReal","Nat","OfNat.ofNat","ProbabilityTheory.HasLaw","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","Real","Real.measurableSpace","congrArg","id","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCIRItoSquare","name":"GinibrePoincare.ginibreOneParticleBrownianPath_CIR_square_leftSums","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex.im","Complex.re","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianOUItoSquareLeftSum","GinibrePoincare.ginibreOneParticleBrownianPath","GinibrePoincare.ginibreOneParticleRadius","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.MeasureSpace.volume","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","NNReal","NNReal.instSemiring","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","PseudoEMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.instZero","Real.measureSpace","Real.metricSpace","Real.normedAddCommGroup","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.left","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex.im","Complex.re","Continuous","Continuous.intervalIntegrable","Continuous.pow","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Filter.EventuallyEq","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.instOfNat","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianOU","GinibrePoincare.ginibreBrownianOUItoSquareLeftSum","GinibrePoincare.ginibreBrownianOUItoSquareLeftSum_tendstoInProbability","GinibrePoincare.ginibreBrownianOU_actual_path","GinibrePoincare.ginibreOneParticleBrownianPath","GinibrePoincare.ginibreOneParticleBrownianPath_radius_quadratic_ae","GinibrePoincare.ginibreOneParticleRadius","GinibrePoincare.ginibreOneParticleRadius._proof_1","GinibrePoincare.ginibre_tendstoInMeasure_add","GinibrePoincare.ginibre_tendstoInMeasure_const_mul","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mat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ginibreOriginalStochasticL2Operator._proof_2","type_dependencies":["And","LE.le","NNReal","NNReal.toReal","OfNat.ofNat","Preorder.toLE","Real","Real.instPreorder","Real.instZero","Zero.toOfNat0"],"value_dependencies":["And.intro","LE.le","NNReal","NNReal.toReal","OfNat.ofNat","Preorder.toLE","Real","Real.instLE","Real.instPreorder","Real.instZero","Subtype.property","Zero.toOfNat0","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Operator","name":"GinibrePoincare.ginibreOriginalStochasticL2Operator._proof_3","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalEquilibriumPathLaw","GinibrePoincare.ginibreOriginalEquilibrium_pathMeasurable","GinibrePoincare.ginibreOriginalStochasticL2Operator._proof_1","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.MeasurePreserving","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","Subtype.mk","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["Fin","GinibrePoincare.ginibreOriginalEndpointInitialMeasurePreserving","LT.lt","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","NNReal","NNReal.toReal","Nat","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","Prod","Real","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Sampling","name":"GinibrePoincare.ginibreOriginalStochasticL2Operator.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.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Group.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","GinibrePoincare.ginibreOriginalStochasticL2Operator_bounded_measurable_pairing","GinibrePoincare.ginibreStationaryContinuousTransitionMean","GinibrePoincare.ginibreStationaryContinuousTransitionMean_eq_original_ae","HMul.hMul","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.instMul","Real.instRCLike","Real.isBoundedSMul","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Real.toNNReal","Real.toNNReal_coe","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Operator","name":"GinibrePoincare.ginibreOriginalStochasticL2Operator_norm_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instLE","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiri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ologicalSpaceSubtype","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Operator","name":"GinibrePoincare.ginibreOriginalStochasticL2Operator_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.one","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And.intro","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.one","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalEndpointInitialMeasurePreserving","GinibrePoincare.ginibreOriginalEndpointTerminalMeasurePreserving","GinibrePoincare.ginibreOriginalEquilibriumPathLaw","GinibrePoincare.ginibreOriginalEquilibrium_pathMeasurable","GinibrePoincare.ginibreOriginalStochasticL2Operator","GinibrePoincare.ginibreOriginalStochasticL2Operator._proof_1","GinibrePoincare.ginibreOriginalStochasticL2Operator._proof_2","GinibrePoincare.ginibreOriginalStochasticL2Operator._proof_3","GinibrePoincare.stationaryEndpointL2Operator","GinibrePoincare.stationaryEndpointL2Pullback","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearIsometry.adjoint_comp_self","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","NNReal.instZero","NNReal.toReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.topologicalSpace","Preorder.toLE","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBounded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eminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Resolvent","name":"GinibrePoincare.ginibreOriginalStochasticL2Resolvent._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent._proof_1","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionCoreResolvent","name":"GinibrePoincare.ginibreOriginalStochasticL2Resolvent.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.rec","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Resolvent","name":"GinibrePoincare.ginibreOriginalStochasticL2Resolvent.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq"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groupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.cast_lt._simp_1","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.measurableSpace","Real.normedAddCommGroup","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toSub","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congr","congrArg","congrFun'","div_pos","fact_one_le_two_ennreal","id","inner_sub_left","instHDiv","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","real_inner_comm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionResolventIdentification","name":"GinibrePoincare.ginibreOriginalStochasticL2Resolvent_eq_analytic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","HDiv.hDiv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instLT","Real.instNatCast","Real.instZero","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHDiv","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero",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","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","Inner.inner","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLT","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreOriginalStochasticL2Operator","GinibrePoincare.ginibreOriginalStochasticL2Operator_symmetric","GinibrePoincare.ginibreOriginalStochasticL2Resolvent","GinibrePoincare.ginibreOriginalStochasticL2Resolvent_pairing","HMul.hMul","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsProbabilityMeasure","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instLT","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.Ioi","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionSymmetricOperator","name":"GinibrePoincare.ginibreOriginalSymmetricStochasticL2Operator","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt"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uousLinearEquiv.piCongrLeft","ContinuousLinearEquiv.piCongrLeft._proof_1","ContinuousLinearEquiv.piCongrLeft._proof_2","ContinuousLinearEquiv.piCongrLeft._proof_3","ContinuousLinearEquiv.piCongrLeft._proof_4","ContinuousLinearEquiv.piCongrLeft._proof_5","ContinuousLinearEquiv.piCongrLeft._proof_6","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.ndrec","Eq.trans","Equiv","Equiv.apply_symm_apply","Equiv.instEquivLike","Equiv.invFun","Equiv.piCongrLeft","Equiv.symm","Equiv.toFun","EquivLike.toFunLike","Fin","Function.LeftInverse","Function.RightInverse","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreParticlePermutationCLM","GinibrePoincare.permute","HAdd.hAdd","HSMul.hSMul","Homeomorph.piCongrLeft","Homeomorph.toEquiv","Homeomorph.toEquiv_piCongrLeft","InnerProductSpace.toNormedSpace","LinearEquiv","LinearEquiv.invFun","LinearEquiv.mk","LinearEquiv.mk.congr_simp","LinearEquiv.toLinearMap","LinearMap","LinearMap.mk","LinearMap.mk.congr_simp","LinearMap.toAddHom","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","SMulZeroClass.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_rec_constant","eq_self","funext","instHAdd","instHSMul","instInnerProductSpaceRealComplex","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalGlobalPathFactorization","name":"GinibrePoincare.ginibrePathCenter","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousMap","ContinuousMap.comp","ContinuousMap.mk","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","GinibrePoincare.ginibrePathCenter._proof_1","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalGlobalPathFactorization","name":"GinibrePoincare.ginibrePathCenter._proof_1","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap.continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.t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Geometry","name":"GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan_le_graded","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instPartialOrder","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePositiveQuotientGradedClosedSpan","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","ClosedSubmodule","ClosedSubmodule.instCompleteLatticeOfT1Space","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientGradedClosedSpan","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpac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actic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fderiv","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGeneratorL2","name":"GinibrePoincare.ginibrePregenerator_eq_zero_of_notMem_tsupport","type_dependencies":["Complex","Complex.instNormedField","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibrePregenerator","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivInvMonoid.toInv","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const_zero","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.configurationLaplacian","GinibrePoincare.coordinateDirection","GinibrePoincare.coulombPairDirection","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibrePregenerator._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.secondDirectionalDerivative","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","LE.le","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedR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EEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.cast_one","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.mul","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormOneClass.norm_one","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRing","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","Subtype","True","True.intro","UniformSpace.toTopologicalSpace","congr","congrArg","congrFun'","eq_self","eq_true","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSMul","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","mul_pow","norm_smul","of_eq_true","one_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionClasses","name":"GinibrePoincare.ginibreRealCenterL2_projectionResidual","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDivInvMonoid","Complex.instField","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSumL2","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealCenterL2","HDiv.hDiv","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerPr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Poincare.ginibreRealPaperSpeedGenerator_scalar_comp","GinibrePoincare.ginibre_centerSquared_gradient_normSq","GinibrePoincare.ginibre_deriv_deriv_log","GinibrePoincare.realGradientNormSq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt.deriv","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","LE.le","LT.lt","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.contDiffAt_log","Real.denselyNormedField","Real.hasDerivAt_log","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.log","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","Sub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,"instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.reCLM","ContinuousLinearMap.comp","ContinuousLinearMap.proj","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreRealParticleCoordinateCLM._proof_1","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreNonsymmetricCounterexample","name":"GinibrePoincare.ginibreRealParticleCoordinateCLM._proof_1","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreNonsymmetricCounterexample","name":"GinibrePoincare.ginibreRealParticleCoordinateCLM.eq_1","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.proj","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreRealParticleCoordinateCLM","GinibrePoincare.ginibreRealParticleCoordinateCLM._proof_1","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearMap","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreRealParticleCoordinateCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreWeakPermutation","name":"GinibrePoincare.ginibreRealPermutationAverageL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddC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oup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_1","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_2","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_3","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_5","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_6","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instCommSemiring","Real.normedField","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid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CommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryGinibreVectorMeasure","name":"GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_1","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_2","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_3","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_5","GinibrePoincare.ginibreResolventVectorSpectralMeasure._proof_6","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.complexToReal","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonU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NonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.measurableSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryGinibreVectorMeasure","name":"GinibrePoincare.ginibreResolventVectorSpectralMeasure_mass","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreResolventVectorSpectralMeasure","GinibrePoincare.ginibreSymmetricL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Real.measurableSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.univ","SetLike.instMembership","Submodule","Submodule.normedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.ring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreFullComplexResolvent_isSelfAdjoint","GinibrePoincare.ginibreFullComplexSymmetric_complete","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreResolventVectorSpectralMeasure","GinibrePoincare.ginibreResolventVectorSp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reMeasure_isProbabilityMeasure","GinibrePoincare.integrable_sq_ginibre","GinibrePoincare.integrable_square_mul_log_ginibre","GinibrePoincare.squareEntropy_nonneg","HasCompactSupport","LT.lt","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticCenterLampertiGenerator","name":"GinibrePoincare.ginibreSquareRootCenter","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquared","Nat","Real.sqrt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterLampertiRegularization","name":"GinibrePoincare.ginibreSquareRootCenter.eq_1","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.ginibreCenterSquared","GinibrePoincare.ginibreSquareRootCenter","Nat","Real","Real.sqrt"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.ginibreSquareRootCenter","Nat","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticSquareRootRadius","name":"GinibrePoincare.ginibreSquareRootRadius","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.pairwiseRadius","Nat","Real.sqrt"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreRadiusNotHolomorphic","name":"GinibrePoincare.ginibreSquaredNormL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofReal","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSquaredNormL2._proof_1","GinibrePoincare.ginibreSquaredNormL2._proof_2","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp.toLp","Nat","OfNat.ofNat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRadiusNotHolomorphic","name":"GinibrePoincare.ginibreSquaredNormL2._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRadiusNotHolomorphic","name":"GinibrePoincare.ginibreSquaredNormL2._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.ofRealCLM","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSquaredNormL2._proof_1","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","Semiring.toNonAssocSemirin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iv","Fintype.card_fin","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.ginibreConstantClosedSubspace","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreFiniteQuotientDegreeZero_eq_constants","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.ginibreSquaredNormL2","GinibrePoincare.ginibreSquaredNormL2_coeFn","GinibrePoincare.ginibreSquaredNormL2_phase_zero","GinibrePoincare.ginibre_ae_eq_iff_volume","GinibrePoincare.ginibre_holomorphic_phase_mem_quotientDegree","HMul.hMul","HSMul.hSMul","Iff.mp","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","LinearIsometry.toLinearMap","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_const","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsOpenPosMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Membership.mem","MonoidHomClass.toOneHomClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MonoidWithZeroHomClass.toZeroHomClass","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NSMul.toSMul","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instOne","Real.instZero","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congrArg","congrFun","congrFun'","continuous_apply","continuous_const","continuous_finsetSum","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instHSMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalRingReal","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","map_one","map_zero","measureSpaceOfInnerProductSpace","mul_one","nsmul_eq_mul","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRadiusNotHolomorphic","name":"GinibrePoincare.ginibreSquaredNormL2_phase_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupCla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","AddZeroClass.toAddZero","Algebra.toSMul","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugation","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module'","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugation","GinibrePoincare.ginibreSymmetricL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivis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ationEquiv._proof_5","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.instNormedAddCommGroup","ContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup.toContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreSymmetricConjugationEquiv._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreSymmetricConjugationEquiv._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugationEquiv._proof_4","GinibrePoincare.ginibreSymmetricConjugationEquiv._proof_5","GinibrePoincare.ginibreSymmetricConjugationEquiv._proof_6","InnerProductSpace.toNormedSpace","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.toSMul","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.Lp.instIsScalarTower","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreSymmetricConjugationEquiv_apply","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugation","GinibrePoincare.ginibreSymmetricConjugationEquiv","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module'","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","EquivLike.toFunLike","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugationEquiv","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module'","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"GinibrePoincare.ginibreSymmetricConjugation_coe","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CStarRing.to_normedStarGroup","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugation","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne"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,"GinibrePoincare.Configuration","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricConjugation","GinibrePoincare.ginibreSymmetricConjugation._proof_1","GinibrePoincare.ginibreSymmetricConjugation._proof_2","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instInvolutiveStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Submodule","Submodule.setLike","Subtype","Subtype.coe_eta","Subtype.ext","Subtype.mk","Subtype.mk.congr_simp","Subtype.val","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","star_star"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison","name":"GinibrePoincare.ginibreSymmetricContractionSemigroup_eq_from_actual_laplace","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instLE","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.Ioi","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.normedAddCommGroup","Submodule.normedSpace","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","And.intro","And.left","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","Continuous","Continuous.comp","Continuous.continuousOn","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.actualContractionLaplace_commutes","GinibrePoincare.actualContractionLaplace_orbit_derivative","GinibrePoincare.ginibreFullGenerator_real_scaled_orbit_unique","GinibrePoincare.ginibreFullRealEvolution","GinibrePoincare.ginibreFullRealEvolution.congr_simp","GinibrePoincare.ginibreFullRealEvolution_continuous_orbit","GinibrePoincare.ginibreFullRealEvolution_preserves_graph","GinibrePoincare.ginibreFullRealEvolution_scaled_graph_derivative","GinibrePoincare.ginibreFullRealEvolution_zero_apply","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreFullSymmetricValues_complete","GinibrePoincare.ginibreFullSymmetric_operators_eq_on_resolvent_range","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSMul.hSMul","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","MulZeroClass.mul_zero","MulZeroClass.toZero","NNReal","NNReal.instIsTopologicalSemiring","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Neg.neg","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","PolynormableSpace.continuousSMul","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Real.toNNReal_coe","Real.toNNReal_zero","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioi","Set.Ioo","Set.instMembership","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Submodule","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.module","Submodule.normedAddCommGroup","Submodule.normedSpace","Submodule.setLike","Submodule.smul","Subtype","Subtype.property","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison.0.GinibrePoincare.ginibreSymmetricContractionSemigroup_eq_from_actual_laplace._abel_1_1","_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison.0.GinibrePoincare.ginibreSymmetricContractionSemigroup_eq_from_actual_laplace._abel_1_2","congr","congrArg","congrFun'","continuous_const","continuous_real_toNNReal","eq_of_heq","eq_self","fact_one_le_two_ennreal","heq_of_eq","id","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instTopologicalSpaceSubtype","le_rfl","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison","name":"GinibrePoincare.ginibreSymmetricContractionSemigroup_eq_paper_evolution","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.measurableSpace","Continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullRealPaperEvolution","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.isBoundedSMul","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.Ioi","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.normedAddCommGroup","Submo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alysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricDivisibleEntireL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative._proof_1","GinibrePoincare.IsGinibreEntireRepresentative._proof_2","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2._proof_1","GinibrePoincare.ginibreSymmetricEntireL2._proof_4","GinibrePoincare.ginibreSymmetricEntireL2._proof_6","GinibrePoincare.ginibreSymmetricEntireL2._proof_7","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","LT.lt","LinearIsometry.toLinearMap","LinearMap.comp","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.comap","Submodule.module","Submodule.setLike","Submodule.subtype","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricDivisibleEntireL2._proof_1","type_dependencies":["Complex","Complex.instSemiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Complex","Complex.instSemiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricDivisibleEntireL2_eq_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","ClosedSubmodule","ClosedSubmodule.instSetLike","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.symm","EquivLike.toFunLike","Exists.casesOn","Exists.intro","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.gaussianAlternatingZeroModeClosedSpan","GinibrePoincare.ComplexHermite.gaussianAlternatingZeroModeClosedSpan_eq_hermiteZeroMode_comap","GinibrePoincare.ComplexHermite.gaussianAlternatingZeroModeClosedSpan_le_hermiteZeroMode","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.ComplexHermite.map_ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianEntireL2","GinibrePoincare.gaussianEntireL2_eq_zeroModeClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.vandermondeSymmetricAlternatingEquiv","Iff","Iff.intro","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearEquiv.toLinearMap","LinearIsometryEquiv","LinearIsometryEquiv.injective","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.toLinearEquiv","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.t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ing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2._proof_5","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricEntireL2._proof_5","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2_eq_divisibleEntire","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative","GinibrePoincare.IsGinibreEntireRepresentative._proof_1","GinibrePoincare.IsGinibreEntireRepresentative._proof_2","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreDivisibleEntire_exists_symmetricRepresentative","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2","GinibrePoincare.ginibreSymmetricDivisibleEntireL2_eq_holomorphic","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricEntireL2._proof_4","GinibrePoincare.ginibreSymmetricEntireL2._proof_6","GinibrePoincare.ginibreSymmetricEntireL2._proof_7","GinibrePoincare.ginibreSymmetricEntireL2_le_holomorphic","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.instPartialOrder","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","le_antisymm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2_eq_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricDivisibleEntireL2","GinibrePoincare.ginibreSymmetricDivisibleEntireL2_eq_holomorphic","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricEntireL2_eq_divisibleEntire","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntireL2_le_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.instPartialOrder","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists.casesOn","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative","GinibrePoincare.IsGinibreEntireRepresentative._proof_1","GinibrePoincare.IsGinibreEntireRepresentative._proof_2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricEntireL2","GinibrePoincare.ginibreSymmetricEntireL2._proof_4","GinibrePoincare.ginibreSymmetricEntireL2._proof_6","GinibrePoincare.ginibreSymmetricEntireL2._proof_7","GinibrePoincare.ginibreSymmetricEntire_mem_holomorphic","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"GinibrePoincare.ginibreSymmetricEntire_mem_holomorphic","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","ClosedSubmodule","ClosedSubmodule.in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","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.intro","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Exists.intro","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.ginibreSymmetricHolomorphicPolynomialClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreEntireRepresentative","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricEntire_mem_holomorphic","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.subtype","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PermutationLp","name":"GinibrePoincare.ginibreSymmetricL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoid.mk","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.mk","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.gaussianPermutationL2._proof_1","GinibrePoincare.gaussianPermutationL2._proof_2","GinibrePoincare.gaussianSymmetricL2._proof_4","GinibrePoincare.gaussianSymmetricL2._proof_5","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePermutationL2","GinibrePoincare.ginibreSymmetricL2._proof_1","GinibrePoincare.ginibreSymmetricL2._proof_2","GinibrePoincare.ginibreSymmetricL2._proof_3","GinibrePoincare.ginibreSymmetricL2._proof_4","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.ofPred","SetLike.instMembership","Submodule.mk","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PermutationLp","name":"GinibrePoincare.ginibreSymmetricL2._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePermutationL2","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiri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SymmetricL2._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePermutationL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePermutationL2","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.instSemilinearIsometryClass","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRi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inibreOUDecay","GinibrePoincare.ginibreTimeChangedOU","HAdd.hAdd","HMul.hMul","NNReal","Real","Real.instAdd","Real.instMul","instHAdd","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.ginibreTimeChangedOU","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUTimeChange","name":"GinibrePoincare.ginibreTimeChangedOU_continuous","type_dependencies":["Continuous","Filter.Eventually","GinibrePoincare.ginibreTimeChangedOU","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","NNReal","NNReal.instTopologicalSpace","ProbabilityTheory.IsBrownianReal","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","Continuous","Continuous.add","Continuous.comp","Continuous.comp'","Continuous.const_mul","Continuous.div_const","Continuous.fun_sub","Continuous.mul","Continuous.rexp","DivInvMonoid.toDiv","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUBrownianClock._proof_1","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreTimeChangedOU","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","NNReal","NNReal.continuous_coe","NNReal.instTopologicalSpace","NNReal.toReal","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.IsBrownianReal.cont","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.exp","Real.instAdd","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instSub","Real.pseudoMetricSpace","Real.toNNReal","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","continuous_const","continuous_id'","continuous_real_toNNReal","id","instHAdd","instHDiv","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUTimeChange","name":"GinibrePoincare.ginibreTimeChangedOU_hasLaw","type_dependencies":["DFunLike.coe","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreTimeChangedOU","MeasurableSpace","MeasureTheory.Measure","NNReal","ProbabilityTheory.HasLaw","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","Real","Real.measurableSpace"],"value_dependencies":["AddGroup.existsAddOfLE","AddMonoid.toAddZeroClass","DFunLike.coe","Distrib.toMul","DistribLattice.toLattice","Eq.mp","GinibrePoincare.ginibreOUBrownianClock","GinibrePoincare.ginibreOUBrownianClock_variance","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreOUTransition","GinibrePoincare.ginibreOUVariance","GinibrePoincare.ginibreTimeChangedOU","HAdd.hAdd","HMul.hMul","HPow.hPow","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","Lattice.toSemilatticeInf","MeasurableSpace","MeasureTheory.Measure","Monoid.toNPow","NNReal","NNReal.instSemiring","NNReal.mk","NPow.toPow","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw._auto_1","ProbabilityTheory.IsPreBrownianReal","ProbabilityTheory.IsPreBrownianReal.hasLaw_eval","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.gaussianReal","ProbabilityTheory.gaussianReal_const_add","ProbabilityTheory.gaussianReal_const_mul","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instMul","Real.instPreorder","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.semiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Zero.toOfNat0","autoParam","congr","congrArg","congrFun'","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instOfNatNat","sq_nonneg","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticOUGaussian","name":"GinibrePoincare.ginibreTimeChangedOU_integral","type_dependencies":["Eq","GinibrePoincare.ginibreOUDecay","GinibrePoincare.ginibreTimeChangedOU","HMul.hMul","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","NNReal","NormedAddCommGroup.toSemi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ulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun'","funext","id","instHAdd","instHMul","instHSMul","instSecondCountableTopologyReal","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticCore","name":"GinibrePoincare.ginibreTransitionAnalyticCore_ito_generator","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.configurationLaplacian","GinibrePoincare.ginibreLangevinDrift","GinibrePoincare.ginibreRealPaperSpeedGenerator","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat"],"value_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreLangevin_fderiv_generator","LT.lt","NNReal","NNReal.toReal","Nat","OfNat.ofNat","Real","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticCore","name":"GinibrePoincare.ginibreTransitionAnalyticCore_right_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreFullCoreSymmetricPregenerator","GinibrePoincare.ginibreFullCoreSymmetricValue","GinibrePoincare.ginibreFullPaperEvolution","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HDiv.hDiv","HSMul.hSMul","HasDerivWithinAt","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.Ici","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHDiv","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreFullCoreSymmetricPregenerator","GinibrePoincare.ginibreFullCoreSymmetricValue","GinibrePoincare.ginibreFullGenerator_core_graph","GinibrePoincare.ginibreFullPaperEvolution_right_derivative","GinibrePoincare.ginibreFullSymmetricOfReal","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticPathLaw","name":"GinibrePoincare.ginibreTransitionAnalyticPathLaw_eq_kernel","type_dependencies":["And","CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","Continuous","DFunLike.coe","Eq","Filter.Eventually","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreBrownianTransitionKernel","GinibrePoincare.ginibreConfigurationBrownianNoise","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.ae","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Subtype","Subtype.instMeasurableSpace","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"],"value_dependencies":["And","CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","Continuous","DFunLike.coe","Eq","Eq.mp","Eq.mpr","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDrivenPath","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreBrownianMaximalProcess_global_pathwise_unique","GinibrePoincare.ginibreBrownianTransitionKernel","GinibrePoincare.ginibreBrownianTransitionKernel_apply_eq_process_law","GinibrePoincare.ginibreConfigurationBrownianNoise","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_congr","MeasureTheory.ae","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.Kernel","ProbabilityTheory.Kernel.instFunLike","ProbabilityTheory.iIndepFun","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","Real.toNNReal","Real.toNNReal_coe","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.instMeasurableSpace","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticWeakCore","name":"GinibrePoincare.ginibreTransitionAnalyticWeakCore_graph_iff","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instA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tAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.module'","Submodule.setLike","Subtype","Subtype.property","Subtype.val","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","congrArg","continuous_const","continuous_fst","continuous_snd","fact_one_le_two_ennreal","id","instArchimedeanNat","instCommCStarAlgebraComplex","instFintypeProd","instHDiv","instHMul","instInhabitedNat","instInnerProductSpaceRealComplex","instIsDirectedOrder","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype","nhds","propext","tendsto_nhds_unique"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticWeakCore","name":"GinibrePoincare.ginibreTransitionAnalyticWeakCore_resolvent","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreFullCoreGradient","GinibrePoincare.ginibreFullCoreValue","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Inner.inner","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHDiv","instHMul","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGro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ompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.continuousOn","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Field.toSemifield","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.Tendsto.eventually_lt_const","Filter.atTop","Filter.eventually_atTop","Finset","Finset.instSetLike","Finset.mem_range","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_le_sum","Finset.sum_range_sub","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GE.ge","GT.gt","GinibrePoincare.ginibreUniformTime","GinibrePoincare.ginibreUniformTime_end","GinibrePoincare.ginibreUniformTime_increment","GinibrePoincare.ginibreUniformTime_mono","GinibrePoincare.ginibreUniformTime_zero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mp","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsCompact.uniformContinuousOn_of_continuous","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.nnrat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","LipschitzOnWith","LipschitzOnWith.norm_sub_le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Metric.tendsto_atTop","Metric.uniformContinuousOn_iff","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","Monotone","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.coe_nonneg","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.instLattice","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.le_of_lt","Nat.le_succ","Nat.rawCast","Nat.succ_le_of_lt","Nat.zero_le","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.dist_eq","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instConditionallyCompleteLinearOrder","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.metricSpace","Real.norm","Real.norm_of_nonneg","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","SemilatticeSup.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformContinuousOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congr","congrArg","congrFun'","dist_eq_norm","div_lt_iff\u2080","div_pos","funext","id","inferInstance","instAddNat","instArchimedeanNat","instClosedIciTopology","instCommSemiringNNRat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instHasSolidNormReal","instInhabitedNat","instIsDirectedOrder","instIsTopologicalRingReal","instLENat","instLTNat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatNat","instOrderTopologyReal","instTransEq","instTransEq_1","instTransLE","instTransLELT","lt_of_not_ge","mul_le_mul","mul_nonneg","mul_one_div","nhds","norm_mul","norm_nonneg","norm_sum_le","normedAlgebraRat","rfl","sub_nonneg","sub_zero","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathQuadraticCross","name":"GinibrePoincare.ginibreUniformQuadraticVariation_add_lipschitz","type_dependencies":["Continuous","EMetricSpace.toPseudoEMetricSpace","Filter.Tendsto","Filter.atTop","Finset.range","Finset.sum","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","LipschitzOnWith","MetricSpace.toEMetricSpace","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.instPreorder","OfNat.ofNat","Pi.instAdd","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instPreorder","Real.instSub","Real.instZero","Real.metricSpace","Real.pseudoMetricSpace","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Continuous","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Filter","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.const_mul","Filter.atTop","Finset","Finset.instSetLike","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.sum_sub_distrib","GinibrePoincare.ginibreUniformQuadraticCross_tendsto_zero","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LipschitzOnWith","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_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OfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","CommSemiring.toSemiring","Complex","Complex.measurableSpace","ContDiff.continuous_deriv","Continuous.comp_aestronglyMeasurable","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.trans","Exists","Exists.casesOn","False","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.sobolevValueTruncation","GinibrePoincare.sobolevValueTruncation_deriv_bound","GinibrePoincare.sobolevValueTruncation_smooth","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","LE.le","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.smul","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.MemLp.const_smul","MeasureTheory.MemLp.of_le","MeasureTheory.ae_of_all","Module.toDistribMulAction","Module.toMulActionWithZero","MonoidWithZero.toMulZeroOneClass","MulActionWithZero.toSMulWithZero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSMulClass","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.smul'","PolynormableSpace.continuousSMul","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulWithZero.toSMulZeroClass","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoidWithZero","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","deriv","id","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPolynormableSpace","instPreorderENat","instTopENat","mul_le_mul_of_nonneg_right","norm_nonneg","norm_smul","not_false_eq_true","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreWeakGradient","name":"GinibrePoincare.ginibreWeakAdjointTest","type_dependencies":["Fin","GinibrePoincare.Configuration","Nat","OfNat.ofNat","Prod","Real","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibreWeakAdjointTest._proof_1","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","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iplierPair._proof_1","GinibrePoincare.ginibreWeakMultiplierPair._proof_2","GinibrePoincare.ginibreWeakMultiplierPair._proof_3","GinibrePoincare.ginibreWeakMultiplierPair._proof_4","GinibrePoincare.ginibreWeakMultiplierPair._proof_5","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MemLp.toLp","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instSMul","WithTop.some","fact_one_le_two_ennreal","instFintypeProd","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevMultipliers","name":"GinibrePoincare.ginibreWeakMultiplierPair._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevMultipliers","name":"GinibrePoincare.ginibreWeakMultiplierPair._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevMultipliers","name":"GinibrePoincare.ginibreWeakMultiplierPair._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevMultipliers","name":"GinibrePoincare.ginibreWeakMultiplierPair._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakMultiplierPair._proof_1","GinibrePoincare.ginibreWeakMultiplierPair._proof_2","GinibrePoincare.ginibreWeakMultiplierPair._proof_3","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.MemLp","Membership.mem"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onoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSpatialCutoff","GinibrePoincare.ginibreSpatialCutoff_compact","GinibrePoincare.ginibreSpatialCutoff_smooth","GinibrePoincare.ginibreWeakMultiplierPair","GinibrePoincare.ginibreWeakSpatialTruncation._proof_1","GinibrePoincare.ginibreWeakSpatialTruncation._proof_2","GinibrePoincare.ginibreWeakSpatialTruncation._proof_3","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevTruncation","name":"GinibrePoincare.ginibreWeakSpatialTruncation._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevTruncation","name":"GinibrePoincare.ginibreWeakSpatialTruncation._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevTruncation","name":"GinibrePoincare.ginibreWeakSpatialTruncation._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakSobolevTruncation","name":"GinibrePoincare.ginibreWeakSpatialTruncation.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakSpatialTruncation","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFu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ul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreDrivenPathRiemann.0.GinibrePoincare.ginibreWeightedIncrements_by_parts._abel_1_1","congr","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHSMul","instHSub","instOfNatNat","of_eq_true","smul_sub","sub_self","sub_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRiemann","name":"GinibrePoincare.ginibreWeightedIncrements_integral_error","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Field.toSemifield","Finset.range","Finset.sum","HAdd.hAdd","HSMul.hSMul","HSub.hSub","HasDerivAt","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMonoid","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHSMul","instHSub","instIsTopologicalRingReal","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","Continuous.intervalIntegrable","Continuous.smul","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","Finset.sum_sub_distrib","GinibrePoincare.ginibreWeightedIncrements_by_parts","HAdd.hAdd","HSMul.hSMul","HSub.hSub","HasDerivAt","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","MeasureTheory.Measure","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Pi.smul'","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCompleteSpace","Real.instMonoid","Real.instRCLike","Real.instSub","Real.lattice","Real.locallyFinite_volume","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.uIcc","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.GinibreDrivenPathRiemann.0.GinibrePoincare.ginibreWeightedIncrements_integral_error._abel_1_1","congrArg","continuous_const","funext","id","instAddNat","instHAdd","instHSMul","instHSub","instIsTopologicalRingReal","instLTNat","instOfNatNat","instPolynormableSpace","intervalIntegral","intervalIntegral.integral_eq_sub_of_hasDerivAt","intervalIntegral.integral_smul_const","intervalIntegral.integral_sub","intervalIntegral.sum_integral_adjacent_intervals","rfl","smul_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRiemann","name":"GinibrePoincare.ginibreWeightedIncrements_integral_error_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","Finset.range","Finset.sum","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasDerivAt","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monotone","Nat","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instSub","Real.instZero","Real.linearOrder","Real.measureSpace","Real.norm","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.uIoc","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instHSMul","instHSub","instIsTopologicalRingReal","instLTNat","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Finset","Finset.instSetLike","Finset.mem_range","Finset.mul_sum","Finset.range","Finset.sum","Finset.sum_le_sum","Finset.sum_range_sub","GinibrePoincare.ginibreWeightedIncrements_integral_error","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasDerivAt","Iff.mp","Iff.mpr","IsModuleTopology.toContinuousSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","Lattice.toSemilatticeInf","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monotone","Nat","Nat.instPreorder","Nat.le_succ","Nat.succ","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measureSpace","Real.norm","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toSeminormedR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sOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasureTheory.MeasureSpace.volume","Membership.mem","Metric.tendsto_atTop","Metric.uniformContinuousOn_iff","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","Monotone","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.instLattice","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.le_succ","Nat.rawCast","Nat.succ","Nat.succ_le_of_lt","Nat.zero_le","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.dist_eq","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instConditionallyCompleteLinearOrder","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioc","Set.instMembership","Set.uIoc","Set.uIoc_of_le","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformContinuousOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonpos","addRightReflectLE_of_addLeftReflectLE","congrArg","congrFun'","contravariant_lt_of_covariant_le","dist_eq_norm","div_lt_iff\u2080","div_pos","id","inferInstance","instAddNat","instArchimedeanNat","instClosedIciTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instHasSolidNormReal","instInhabitedNat","instIsDirectedOrder","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatNat","instOrderTopologyReal","instTransEq","intervalIntegral","le_rfl","lt_of_not_ge","mul_nonneg_of_nonpos_of_nonpos","neg_neg_of_pos","nhds","norm_nonneg","rfl","sub_nonpos"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathUniformPartition","name":"GinibrePoincare.ginibreWeightedUniformIncrements_tendsto_integral","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","Filter.Tendsto","Filter.atTop","Finset.range","Finset.sum","GinibrePoincare.ginibreUniformTime","HAdd.hAdd","HSMul.hSMul","HSub.hSub","HasDerivAt","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LE.le","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Nat","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHSMul","instHSub","instIsTopologicalRingReal","instOfNatNat","intervalIntegral","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toModule","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Continuous","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","Eq.le","Eq.mp","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.mul","Filter.atTop","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ginibreUniformTime","GinibrePoincare.ginibreUniformTime_end","GinibrePoincare.ginibreUniformTime_increment","GinibrePoincare.ginibreUniformTime_mono","GinibrePoincare.ginibreUniformTime_zero","GinibrePoincare.ginibreWeightedIncrements_tendsto_integral","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","HasDerivAt","IsModuleTopology.toContinuousSMul","IsScalarTower.nnrat","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LE.le","LT.lt","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","Nat","Nat.cast","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","instAddNat","instCommSemiringNNRat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","mul_one_div","nhds","normedAlgebraRat","tendsto_const_nhds","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticWeightedSumMemLp","name":"GinibrePoincare.ginibreWeightedUniformLeftSum_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.brownianUniformLeftSum","LE.le","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure","MeasureTheory.MemLp","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.norm","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toNonUnitalCommRing","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENormedAddCommMonoid.toESeminormedAddCommMonoid","Finset","Finset.instSetLike","Finset.range","GinibrePoincare.actualBoundedMultiplier_memLp_two","GinibrePoincare.brownianUniformLeftSum","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HMul.hMul","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.MemLp.sub","MeasureTheory.memLp_finsetSum","Membership.mem","NNReal","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toENormedAddCommMonoid","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instLE","Real.instMul","Real.instSub","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","UniformSpace.toTopologicalSpace","id","instAddNat","instHAdd","instHMul","instHSub","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreZeroPairAvoidance","name":"GinibrePoincare.ginibreZeroPairAvoidanceCutoff","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["Eq","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configur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ibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreEuclideanGradient_norm_sq","GinibrePoincare.ginibreGradientPermutationL2","GinibrePoincare.ginibreGradientPermutationL2._proof_13","GinibrePoincare.ginibreGradientPermutationL2._proof_14","GinibrePoincare.ginibreGradientPermutationL2._proof_16","GinibrePoincare.ginibreGradientPermutationL2._proof_19","GinibrePoincare.ginibreL2Mean","GinibrePoincare.ginibreL2Mean._proof_1","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreL2Variance.eq_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealConstantL2","GinibrePoincare.ginibreRealConstantL2._proof_1","GinibrePoincare.ginibreRealConstantL2_ae","GinibrePoincare.ginibreRealPermutationL2","GinibrePoincare.ginibreRealPermutationL2._proof_1","GinibrePoincare.ginibreRealPermutationL2_ae","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.ginibreWeakEnergy._proof_1","GinibrePoincare.ginibreWeakEnergy.eq_1","GinibrePoincare.ginibre_C1_distributional_gradient","GinibrePoincare.ginibre_distributional_gradient_unique","GinibrePoincare.ginibre_measurePreserving_permute","GinibrePoincare.ginibre_symmetric_weak_poincare","GinibrePoincare.integral_norm_sq_eq_L2_norm_sq","GinibrePoincare.integral_square_eq_L2_norm_sq","GinibrePoincare.permute","GinibrePoincare.realGradientNormSq","GinibrePoincare.smoothGinibreMean","GinibrePoincare.smoothGinibreVariance","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsTopologicalAddGroup.toContinuousAdd","LE","LE.le","LT.lt","LinearIsometry","LinearIsometry.instFunLike","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_sub","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.isBoundedSMul","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","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","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Compl.compl","ContinuousSMul","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","EMetricSpace.metrizableSpace","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HPow.hPow","HasDerivAt","HasDerivAt.congr_of_eventuallyEq","HasDerivAt.const_mul","HasDerivAt.deriv","HasDerivAt.inv","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOpen.mem_nhds","LT.lt","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.NF.pow_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_ofNat","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","MetricSpace.toEMetricSpace","Module","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Ne","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instInv","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.hasDerivAt_sqrt","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","R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Monoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","Trans.trans","True","UniformSpace.toTopologicalSpace","WithLp.ofLp","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","continuous_const","eq_self","fact_one_le_two_ennreal","fderiv","id","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instTransEq","instZeroENat","measureSpaceOfInnerProductSpace","mul_assoc","mul_neg","not_false_eq_true","of_eq_true","rfl","tsupport","tsupport_fderiv_apply_subset"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakGradientSupport","name":"GinibrePoincare.ginibre_distributional_gradient_exists_supported_representative","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.instNormedField","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreMeasure","HasCompactSupport","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.addCommGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instZero","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","And.intro","Classical.propDecidable","Complex","Complex.instNormedField","Complex.measurableSpace","Decidable.byContradiction","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","EuclideanSpace","Exists.intro","False","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_distributional_gradient_zero_off_support","HasCompactSupport","IsCompact.of_isClosed_subset","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Pi.addCommGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instZero","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","Zero.toOfNat0","closure_minimal","congr","congrArg","congrFun'","dite","eq_false","eq_self","fact_one_le_two_ennreal","id","instFintypeProd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","isClosed_tsupport","not_false_eq_true","of_eq_true","tsupport"]},{"kind":"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emiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","congr","congrArg","congrFun'","eq_self","fderiv","funext","id","instCommCStarAlgebraComplex","instContinuousSMulForall","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","of_eq_true","rfl","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRadialGradient","name":"GinibrePoincare.ginibre_fderiv_complexRadius_ofReal","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.pairwiseRadius","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instT2Space","Complex.ofRealCLM","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","DifferentiableAt.hasFDerivAt","DistribMulAction.toMulAction","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ginibre_contDiff_pairwiseRadius","GinibrePoincare.pairwiseRadius","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMono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MetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddGroup","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","fderiv","id","instCommCStarAlgebraComplex","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","neg_sub","one_mul","starRingEnd","sub_neg_eq_add","sub_self","two_mul","zero_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRadialGradient","name":"GinibrePoincare.ginibre_fderiv_pairwiseRadius_real","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.pairwiseRadius","GinibrePoincare.realCoordinateDirection","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instNormedField","Complex.instStarRing","Complex.ofReal","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Eq","Eq.mp","Eq.mpr","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.complexRadius","GinibrePoincare.ginibre_fderiv_complexRadius_ofReal","GinibrePoincare.pairwiseRadius","GinibrePoincare.radius_gradient_real","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","congrArg","fderiv","id","instCommCStarAlgebraComplex","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","starRingEnd","two_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterLampertiNoiseCoefficient","name":"GinibrePoincare.ginibre_fderiv_squareRootCenter","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","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ilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Nat.recAux","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Not.intro","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_self","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","neg_eq_zero","of_eq_true","rfl","sub_eq_zero_of_eq","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGraphNormEquivalence","name":"GinibrePoincare.ginibre_gradient_graph_norm_constants_pos","type_dependencies":["And","LT.lt","Max.max","Min.min","OfNat.ofNat","One.toOfNat1","Real","Real.instLT","Real.instMax","Real.instMin","Real.instOne","Real.instZero","Real.sqrt","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","And.intro","Bool","Eq.refl","Iff.mpr","LT.lt","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Max.max","Min.min","Nat","Nat.ble","Nat.cast_one","OfNat.ofNat","One.toOfNat1","Real","Real.instIsOrderedRing","Real.instLT","Real.instMax","Real.instMin","Real.instNontrivial","Real.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_pos","Ring.toAddGroupWithOne","Zero.toOfNat0","instOfNatNat","lt_max_of_lt_left","lt_min"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGraphNormEquivalence","name":"GinibrePoincare.ginibre_gradient_graph_norm_equivalence","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincar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rePoincare.ginibreContinuousNoiseCenter","GinibrePoincare.ginibreContinuousNoiseCenter_continuous","GinibrePoincare.ginibreDrivenGlobalPathElement","GinibrePoincare.ginibreEquilibriumPath","GinibrePoincare.ginibreEquilibriumPath_measurable","GinibrePoincare.ginibreFreeInitialVersion","GinibrePoincare.ginibreOUPathElement","GinibrePoincare.ginibreOUPathElement_measurable","GinibrePoincare.ginibrePathCenter","GinibrePoincare.ginibrePathCenter_measurable","GinibrePoincare.independentInitialCenterPathBorel","GinibrePoincare.independentInitialCenterPathSpace","GinibrePoincare.instBorelSpaceGinibreContinuousNoise","GinibrePoincare.instMeasurableSpaceContinuousMapRealComplex_ginibrePoincare_2","GinibrePoincare.instMeasurableSpaceContinuousMapRealComplex_ginibrePoincare_3","GinibrePoincare.instMeasurableSpaceContinuousMapRealConfiguration","GinibrePoincare.instMeasurableSpaceGinibreContinuousNoise","GinibrePoincare.instTopologicalSpaceGinibreContinuousNoise","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.recenteredConfiguration","Iff.mpr","LT.lt","Measurable","Measurable.comp","Measurable.prodMk","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.ae_prod_iff_ae_ae","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","Membership.mem","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","Not","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","StandardBorelSpace.instMeasurableEq","Subtype","Subtype.mk","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","dite_eq_left_of_eq_true","eq_self","eq_true","funext","id","instCommCStarAlgebraComplex","instIsTopologicalAddGroupReal","instLTNat","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instProperSpaceReal","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableSet_eq_fun","measurable_fst","measurable_snd","of_eq_true","secondCountable_of_proper","standardBorel_of_polish"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalIndependentInitial","name":"GinibrePoincare.ginibre_independentInitial_path_eq_original","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.measurableSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Filter.Eventually","Fin","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreBrownianMaximalProcess","GinibrePoincare.ginibreEquilibriumPath","GinibrePoincare.recenteredConfiguration","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.ae","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","ProbabilityTheory.IndepFun","ProbabilityTheory.IsBrownianReal","ProbabilityTheory.iIndepFun","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.pseudoMetricSpace","Real.toNNReal","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instLTNat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","Classical.propDecidable","CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Continuous","ContinuousMap","ContinuousMap.const","ContinuousMap.instFunLike","ContinuousMap.mk","ContinuousMap.mk.congr_simp","DFunLike.coe","Decidable","EMetric.instIsCountablyGeneratedUniformity","EMet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","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toENormedAddCommMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instInv","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","SetLike.instMembership","Subtype.fintype","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","instDecidableEqFin","instDecidableNot","instFintypeProd","instIsTopologicalRingReal","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianKilledMixtureIntegration","name":"GinibrePoincare.ginibre_killed_product_mixture","type_dependencies":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instOne","ENNReal.instZero","ENNReal.measurableSpace","Eq","Filter.Eventually","HMul.hMul","Measurable","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.SFinite","MeasureTheory.ae","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Set","Set.indicator","instDistribOfSemiring","instHMul"],"value_dependencies":["Classical.propDecidable","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instMeasurableMul\u2082","ENNReal.instOne","ENNReal.instZero","ENNReal.measurableSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","Function.comp","HMul.hMul","Inter.inter","Measurable","Measurable.aemeasurable","Measurable.comp","Measurable.const_mul","Measurable.indicator","MeasurableMul\u2082.toMeasurableMul","MeasurableSet","MeasurableSet.inter","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.ext","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.prod","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_apply","MeasureTheory.Measure.restrict_apply_univ","MeasureTheory.Measure.withDensity","MeasureTheory.SFinite","MeasureTheory.ae","MeasureTheory.lintegral","MeasureTheory.lintegral_congr","MeasureTheory.lintegral_congr_ae","MeasureTheory.lintegral_const","MeasureTheory.lintegral_const_mul","MeasureTheory.lintegral_indicator","MeasureTheory.lintegral_map","MeasureTheory.lintegral_prod","MeasureTheory.withDensity_apply","Membership.mem","MulZeroOneClass.toMulOneClass","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSemiring.toSemigroupWithZero","Not","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Semigroup.toMul","SemigroupWithZero.toSemigroup","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instInter","Set.instMembership","Set.mem_preimage._simp_1","Set.ofPred","Set.preimage","Set.univ","True","Zero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreHamiltonianKilledMixtureIntegration.0.GinibrePoincare.ginibre_killed_product_mixture._simp_1_1","congr","congrArg","congrFun'","dite","eq_false","eq_self","funext","id","instDistribOfSemiring","instHMul","instMulZeroOneClassOfSemiring","measurable_fst","measurable_prodMk_left","not_false_eq_true","of_eq_true","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianInitialMeasureIdentification","name":"GinibrePoincare.ginibre_lintegral_completion","type_dependencies":["ENNReal","ENNReal.measurableSpace","Eq","Measurable","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.completion","MeasureTheory.NullMeasurableSpace","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","MeasureTheory.lintegral"],"value_dependencies":["ENNReal","ENNReal.measurableSpace","Eq","Eq.mp","Eq.symm","GinibrePoincare.ginibre_map_completion","Measurable","Measurable.nullMeasurable","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.completion","MeasureTheory.Measure.map","MeasureTheory.Measure.map_id","MeasureTheory.NullMeasurable.measurable'","MeasureTheory.NullMeasurableSpace","MeasureTheory.NullMeasurableSpace.instMeasurableSpace","MeasureTheory.lintegral","MeasureTheory.lintegral_map","congrArg","id","measurable_id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGinibreSpectralLaw","name":"GinibrePoincare.ginibre_lintegral_diagonal_density","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.schurDiagonalSpectralDensity","HDiv.hDiv","HMul.hMul","HPow.hPow","Inv.inv","LT.lt","Measurable","MeasurableSpace.pi","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.pi","instDistribOfSemiring","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommMagma.to_isCommutative","CommRing.toNonUnitalCommRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous.measurable","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instMeasurableMul\u2082","ENNReal.measurableSpace","ENNReal.measurable_ofReal","ENNReal.ofReal","ENNReal.ofReal_mul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianDensity","GinibrePoincare.complexGaussianDensityIdentification","GinibrePoincare.complexGaussianDensityMeasure","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationNormSq","GinibrePoincare.configurationVolume","GinibrePoincare.continuous_vandermonde","GinibrePoincare.gaussianWeight","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure._proof_1","GinibrePoincare.ginibreMeasure.eq_1","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.measurable_complexGaussianDensity","GinibrePoincare.measurable_schurDiagonalSpectralDensity","GinibrePoincare.rawGinibreMeasure","GinibrePoincare.rawGinibreMeasure.eq_1","GinibrePoincare.schurDiagonalSpectralDensity","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeWeight","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Inv.inv","IsMulCommutative.is_comm","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","LT.lt.le","Lean.Data.AC.Context.eq_of_norm","Lean.Data.AC.Context.mk","Lean.Data.AC.Expr.op","Lean.Data.AC.Expr.var","Lean.Data.AC.Variable","Lean.Data.AC.Variable.mk","List.cons","List.nil","Measurable","Measurable.comp","Measurable.mul","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","MeasureTheory.lintegral_const_mul","MeasureTheory.lintegral_smul_measure","MeasureTheory.lintegral_withDensity_eq_lintegral_mul","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSemiring.toSemigroupWithZero","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Option.none","Option.some","PLift","PLift.up","PartialOrder.toPreorder","Pi.instMul","Pi.opensMeasurableSpace","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instSemigroup","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.measurableSpace","Real.partialOrder","Real.pi","Real.pi_pos","Real.pseudoMetricSpace","Real.semiring","Semifield.toDivisionSemiring","Semigroup.toMul","Semigroup.to_isAssociative","SemigroupWithZero.toSemigroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Std.Commutative","Std.IdempotentOp","Std.LawfulIdentity","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","div_nonneg","funext","id","instCommCStarAlgebraComplex","instCountableFin","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace","mul_assoc","pow_nonneg","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticCenterLogRegularization","name":"GinibrePoincare.ginibre_log_shift_derivatives","type_dependencies":["And","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","HAdd.hAdd","HPow.hPow","Inv.inv","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instInv","Real.instLT","Real.instMonoid","Real.instNeg","Real.instZero","Real.log","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","instHAdd","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Continuous.add","Continuous.continuousAt","ContinuousAt.eventually_ne","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","EMetricSpace.metrizableSpace","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Function.comp","HAdd.hAdd","HDiv.hDiv","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HPow.hPow","HasDerivAt","HasDerivAt.add_const","HasDerivAt.comp","HasDerivAt.congr_of_eventuallyEq","HasDerivAt.deriv","HasDerivAt.inv","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","InvolutiveNeg.toNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","Membership.mem","MetricSpace.toEMetricSpace","Module","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Ne","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.instInv","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.hasDerivAt_log","Real.instAdd","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLT","Real.instMonoid","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.log","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring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igroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Complex.re","ContDiff","ContinuousLinearMap.contDiff","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Fin.mk","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreRealParticleCoordinateCLM","GinibrePoincare.ginibre_coordinate_re_energy","GinibrePoincare.ginibre_coordinate_re_gradient_integrable","GinibrePoincare.ginibre_coordinate_re_integrable","GinibrePoincare.ginibre_coordinate_re_sq_integrable","GinibrePoincare.ginibre_coordinate_re_variance","GinibrePoincare.realGradientNormSq","GinibrePoincare.smoothGinibreEnergy","GinibrePoincare.smoothGinibreVariance","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.ne'","LinearOrder.toPartialOrder","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_pos","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.le_eq_cancel_le","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.Integrable","Monoid.toNPow","MonoidWit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ifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.pairwiseRadius","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instSemiring","Complex.instStarRing","Complex.mul_conj","Complex.mul_re","Complex.normSq","Complex.ofReal","Complex.re","Complex.re_sum","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.centeredScaled_norm_sum","GinibrePoincare.complexRadius","GinibrePoincare.ginibre_fderiv_pairwiseRadius_imaginary","GinibrePoincare.ginibre_fderiv_pairwiseRadius_real","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.pairwiseRadius","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.mul_zero","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.normedField","Real.pse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rePoincare.IsGinibreDistributionalGradient","GinibrePoincare.coordinatePhase","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreDirectionCoefficient","GinibrePoincare.ginibreGradientPhasePullback","GinibrePoincare.ginibreGradientPhasePullback_norm_sq","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_radial_weak_gradient_phase_covariance","HMul.hMul","HPow.hPow","Iff.mp","IsOrderedRing.toMulPosMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PiLp.ext","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instOne","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.ofLp","congrArg","fact_one_le_two_ennreal","id","instFintypeProd","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","norm_nonneg","sq_eq_sq\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakGradientPhase","name":"GinibrePoincare.ginibre_radial_weak_gradient_phase_covariance","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.Eventually","Filter.EventuallyEq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.coordinatePhase","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreDirectionCoefficient","GinibrePoincare.ginibreMeasure","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instMul","Real.instOne","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.ofLp","fact_one_le_two_ennreal","instFintypeProd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","And.left","And.right","ChainCompletePartialOrder.instOfCompleteLatti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oid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNatCast","Complex.instZero","Complex.ofReal","Complex.ofReal_inj._simp_1","Complex.ofReal_injective","Complex.ofReal_sum","Decidable.byContradiction","Decidable.decide","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionMonoid.toInvolutiveInv","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.intro","False","False.elim","Field.toDivisionRing","Field.toSemifield","Fin","Fin.ext","Fin.fintype","Fin.mk","Fin.val","Finset","Finset.card","Finset.card_univ","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.sum_sub_distrib","Finset.univ","Fintype.card","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.Injective","Function.swap","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreCurvaturePairDirection","GinibrePoincare.ginibreCurvaturePairDirection_norm","GinibrePoincare.ginibreCurvaturePairDirection_sum","GinibrePoincare.ginibreHamiltonian","GinibrePoincare.ginibreHamiltonian_pair_direction_le","GinibrePoincare.secondDirectionalDerivative","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasDistribNeg.toInvolutiveNeg","Iff.mp","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","InvolutiveNeg.toNeg","IsCancelMulZero.toIsLeftCancelMulZero","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_natCast","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.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,"instTopologicalSpaceProd","instTransEq","isClosed_Ici","le_of_not_gt","neg_eq_zero","nhds","of_eq_true","rfl","sq_nonneg","sub_eq_zero_of_eq","sub_nonneg._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticProbabilityOperations","name":"GinibrePoincare.ginibre_tendstoInMeasure_add","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","HAdd.hAdd","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","PseudoEMetricSpace.toUniformSpace","Real","Real.instAdd","Real.metricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","instHAdd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","And","And.left","And.right","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Decidable.byContradiction","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.add","Filter.atTop","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.real","MeasureTheory.TendstoInMeasure","MeasureTheory.measureReal_mono","MeasureTheory.measureReal_nonneg","MeasureTheory.measureReal_union_le","MeasureTheory.measure_ne_top","MeasureTheory.tendstoInMeasure_iff_measureReal_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","Mul","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul","Nat.rawC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italNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.toUniformSpace","PseudoEMetricSpace.toWeakPseudoEMetricSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.decidableEq","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instZero","Real.linearOrder","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.ext","Set.instEmptyCollection","Set.instMembership","Set.mem_setOf_eq","Set.ofPred","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","T5Space.toT1Space","T6Space.toT5Space","True","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreStochasticProbabilityOperations.0.GinibrePoincare.ginibre_tendstoInMeasure_const_mul._simp_1_1","congr","congrArg","congrFun'","dite","div_le_iff\u2080","div_pos","eq_false","eq_of_heq","eq_self","funext","id","instArchimedeanNat","instHDiv","instHMul","instHSub","instInhabitedNat","instIsDirectedOrder","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instT6SpaceOfMetrizableSpace","mul_comm","nhds","norm_mul","norm_pos_iff","norm_zero","not_le","of_eq_true","propext","sub_self","tendsto_const_nhds_iff._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticProbabilityRestriction","name":"GinibrePoincare.ginibre_tendstoInMeasure_indicator","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","PseudoEMetricSpace.toUniformSpace","Real","Real.instZero","Real.metricSpace","Set","Set.indicator","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Classical.propDecidable","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.trans","False.elim","Filter.Tendsto","Filter.atTop","HSub.hSub","Iff.mpr","LE.le","LT.lt","LinearOrder.toPartialOrder","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.real","MeasureTheory.TendstoInMeasure","MeasureTheory.measureReal_mono","MeasureTheory.measureReal_nonneg","MeasureTheory.measure_ne_top","MeasureTheory.tendstoInMeasure_iff_measureReal_norm","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.toUniformSpace","PseudoEMetricSpace.toWeakPseudoEMetricSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.instLT","Real.instSub","Real.instZero","Real.linearOrder","Real.metricSpace","Real.norm","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instLE","Set.instMembership","Set.mem_setOf_eq","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero","Zero.toOfNat0","congr","congrArg","dite","id","instHSub","nhds","norm_zero","not_le","propext","squeeze_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticProbabilityOperations","name":"GinibrePoincare.ginibre_tendstoInMeasure_neg","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.atTop","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.TendstoInMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","Neg.neg","PseudoEMetricSpace.toUniformSpace","Real","Real.instNeg","Real.metricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.trans","Filter","Filter.Tendsto","Filter.atTop","HSub.hSub","LE.le","LT.lt","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.real","MeasureTheory.TendstoInMeasure","MeasureTheory.tendstoInMeasure_iff_measureReal_norm","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoEMetricSpace.toUniformSpace","PseudoEMetricSpace.toWeakPseudoEMetricSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instLE","Real.instLT","Real.instNeg","Real.instZero","Real.metricSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.ofPred","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","congrArg","congrFun'","funext","id","instHSub","neg_sub_neg","nhds","norm_sub_rev","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticMeanSquareInProbability","name":"GinibrePoincare.ginibre_tendstoInMeasure_of_meanSquare","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.Tendsto","Filter.atTop","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.TendstoInMeasure","MeasureTheory.integral","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instHPow","instHSub","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Bool","Bool.false","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Filter","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.div_const","Filter.atTop","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Iff.intro","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeft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","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Algebra.id","And","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.measurableSpace","ContDiff","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Exists","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialMollifierKernel","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.convolution","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.addCommGroup","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Set","Set.instLE","Set.ofPred","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithTop.some","fact_one_le_two_ennreal","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instTopologicalSpaceProd","measureSpaceOfInnerProductSpace","nhds","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.id","And","And.casesOn","And.intro","And.left","And.right","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.measurableSpace","ContDiff","Continuous.continuousAt","Continuous.tendsto","ContinuousAt.tendsto","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instTop","ENat","Eq","Eq.mp","EuclideanSpace","Exists","Exists.casesOn","Exists.intro","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.prodMk_nhds","Filter.atTop","Fin","Fin.fintype","Function.comp","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.ginibreEuclideanGradient","GinibrePoincare.ginibreL2OfLebesgue","GinibrePoincare.ginibreL2OfLebesgue_ae","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_le_finite_smul_volume","GinibrePoincare.ginibre_radial_interior_mollification_gradient_memLp","GinibrePoincare.ginibre_radial_interior_sobolev_mollification_exists","GinibrePoincare.memLp_radial_convolution_compact","GinibrePoincare.radialMollifierKernel","GinibrePoincare.radialSmoothCompactMollificatio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Normed","InnerProductSpace.gramSchmidtNormed.eq_1","InnerProductSpace.gramSchmidt_def","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsEmpty.forall_iff._simp_1","IsOrderedAddMonoid.toAddLeftMono","IsUnit","LT.lt","LT.lt.ne","LT.lt.ne'","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LocallyFiniteOrderBot","Membership.mem","Module","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulAction.toSemigroupAction","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","NormedSpace.toNormSMulClass","Not","OfNat.ofNat","One.toOfNat1","Orthonormal","Orthonormal.norm_eq_one","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.ofReal","RCLike.ofReal_one","RCLike.toDenselyNormedField","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.semiring","Ring.toAddGroupWithOne","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Finite.fintype","Set.Iio","Set.ext","Set.finite_Iio","Set.image","Set.instMembership","Set.instSingletonSet","Set.mem_Iio._simp_2","Set.mem_image._simp_1","Set.mem_range._simp_1","Set.range","SetLike.instMembership","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Submodule","Submodule.HasOrthogonalProjection","Submodule.HasOrthogonalProjection.ofCompleteSpace","Submodule.mem_span_range_iff_exists_fun","Submodule.setLike","Submodule.span","Submodule.span_singleton_smul_eq","Submodule.starProjection","Submodule.starProjection.congr_simp","Submodule.starProjection_singleton","Subtype","Subtype.exists._simp_1","Subtype.ext","Subtype.mk","Subtype.property","Subtype.pseudoMetricSpace","Subtype.val","True","UniformSpace.toTopologicalSpace","WellFounded.induction","WellFoundedLT","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryTriangularGramSchmidt.0.GinibrePoincare.gramSchmidtNormed_of_positive_triangular._abel_1_1","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryTriangularGramSchmidt.0.GinibrePoincare.gramSchmidtNormed_of_positive_triangular._abel_1_2","abs","abs_of_pos","complete_of_proper","congr","congrArg","congrFun'","div_one","eq_false","eq_self","exists_prop._simp_1","exists_prop_congr","forall_congr","funext","id","iff_self","implies_congr","implies_true","inner_add_right","inner_smul_right","inner_sum","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsEmptyFalse","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","inv_mul_cancel\u2080","isUnit_iff_ne_zero","ite","ite_eq_left_of_eq_true","ite_eq_right","ite_eq_right_of_eq_false","mul_one","norm_smul","not_false_eq_true","not_true_eq_false","of_eq_true","one_pow","one_smul","orthonormal_iff_ite","propext","rfl","smul_smul","wellFounded_lt","zero_add"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialGeneratorSpectrum","name":"GinibrePoincare.graphOperatorSpectrum","type_dependencies":["Complex","Complex.instNormedField","Complex.instRing","Complex.instSemiring","LinearPMap","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","RingHom.id","Semiring.toNonAssocSemiring","Set"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRing","Complex.instSemiring","GinibrePoincare.HasBoundedGraphResolvent","LinearPMap","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","Not","RingHom.id","Semiring.toNonAssocSemiring","Set.ofPred"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.groundStateAdmissibility","type_dependencies":["GinibrePoincare.GroundStateAdmissibilityStatement"],"value_dependencies":["And","And.intro","And.left","And.right","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.ofRea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toStarRing","Real","Real.commRing","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.sqrt","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","TrivialStar.star_trivial","WithLp.ofLp","congr","congrArg","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHMul","instOfNatAtLeastTwo","instOfNatNat","instTrivialStarReal","mul_comm","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUECenterWitness","name":"GinibrePoincare.gueCenterCoordinate_gradient","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueCenterCoordinate","GinibrePoincare.gueCenterUnit","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","fact_one_le_two_ennreal","gradient","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.fderiv","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","EquivLike.toFunLike","EuclideanSpace","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.gueCenterCoordinate","GinibrePoincare.gueCenterUnit","HasGradientAtFilter._proof_1","HasGradientAtFilter._proof_2","HasGradientAtFilter._proof_3","HasGradientAtFilter._proof_4","HasGradientAtFilter._proof_5","InnerProductSpace.toDual","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","LinearIsometryEquiv.symm_apply_apply","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instCompleteSpace","Real.instRCLike","Real.instRing","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCo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ow","instHSMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_one","of_eq_true","one_pow","real_inner_self_eq_norm_sq","real_inner_smul_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUECenterSplit","name":"GinibrePoincare.gueCenterLineIsometry._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.gueCenterLine","GinibrePoincare.gueCenterLineIsometry._proof_1","GinibrePoincare.gueCenterLineIsometry._proof_2","GinibrePoincare.gueCenterLineIsometry._proof_3","GinibrePoincare.gueCenterLineIsometry._proof_4","GinibrePoincare.gueCenterLineIsometry._proof_5","GinibrePoincare.gueCenterUnit","HSMul.hSMul","Inner.inner","InnerProductSpace.toInner","LT.lt","LinearEquiv","LinearEquiv.mk","LinearMap.mk","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instSMul","fact_one_le_two_ennreal","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.gueCenterLine","GinibrePoincare.gueCenterLineIsometry._proof_1","GinibrePoincare.gueCenterLineIsometry._proof_2","GinibrePoincare.gueCenterLineIsometry._proof_3","GinibrePoincare.gueCenterLineIsometry._proof_4","GinibrePoincare.gueCenterLineIsometry._proof_5","GinibrePoincare.gueCenterUnit","GinibrePoincare.gueCenterUnit_norm","HMul.hMul","HSMul.hSMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","LT.lt","LinearEquiv","LinearEquiv.mk","LinearMap.mk","Membership.mem","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.instNormSMulClass","PiLp.seminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instMul","Real.instOne","Real.instRCLike","Real.instRing","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instSMul","congrArg","fact_one_le_two_ennreal","id","instHMul","instHSMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_one","norm_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUECenterSplit","name":"GinibrePoincare.gueCenterLineIsometry._proof_7","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat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inibrePoincare.gueDoubledOrderedExpectation._proof_2","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","MeasurableSpace.pi","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","Real","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.borelSpace","PiLp.innerProductSpace._proof_1","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","Real","Real.borelSpace","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCountableFin","instCountableProd","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceGUENormalization","name":"GinibrePoincare.gueDoubledOrderedMeasure","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","MeasurableSpace.pi","MeasureTheory.Measure","Nat","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","Real","Real.measurableSpace","WithLp.measurableSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.ofReal","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueDoubledOrderedDensity","GinibrePoincare.gueDoubledOrderedMeasure._proof_1","GinibrePoincare.gueDoubledOrderedMeasure._proof_2","GinibrePoincare.gueDoubledOrderedMeasure._proof_3","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","WithLp.measurableSpace","fact_one_le_two_ennreal","instDistribOfSemiring","instFintypeProd","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUENormalization","name":"GinibrePoincare.gueDoubledOrderedMeasure._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","InnerProductSpace.toNormedSpace","Module.Finite","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.innerProductSpace._proof_1","Prod","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","WithLp","WithLp.instAddCommGroup","WithLp.instModule","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.innerProductSpace._proof_1","Prod","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","WithLp.instModuleFinite","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUENormalization","name":"GinibrePoincare.gueDoubledOrderedMeasure._proof_2","type_d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","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrthonormalBasis","OrthonormalBasis.instFunLike","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.one","congrArg","fact_one_le_two_ennreal","funext","gradient","id","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","stdOrthonormalBasis"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUENormalization","name":"GinibrePoincare.gueDoubledOrderedMeasure_integral","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.gueDoubledOrderedDensity","GinibrePoincare.gueDoubledOrderedMeasure","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instDivInvMonoid","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","fact_one_le_two_ennreal","instCountableFin","instCountableProd","instFintypeProd","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","BorelSpace.opensMeasurable","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Continuous.measurable","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","ENNReal.ofReal_lt_top","ENNReal.toReal","ENNReal.toReal_inv","ENNReal.toReal_ofReal","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","EuclideanSpace","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","Finite.instProd","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gueDoubledOrderedDensity","GinibrePoincare.gueDoubledOrderedDensity_continuous","GinibrePoincare.gueDoubledOrderedDensity_nonneg","GinibrePoincare.gueDoubledOrderedMeasure","GinibrePoincare.gueDoubledOrderedMea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OfNatNat","instOneENat","instZeroENat","map_zero","norm_zero","not_false_eq_true","of_eq_true","smulCommClass_self","starRingEnd","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricInequalities","name":"GinibrePoincare.gueFullMeasure_symmetric_square_lsi_compactC1","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Equiv.Perm","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueFullMeasure","GinibrePoincare.guePermute","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","WithTop","WithTop.one","fact_one_le_two_ennreal","gradient","instHDiv","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddUnits","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","ContDiff","ContDiff.continuous","ContDiff.fderiv_right","Continuous","Continuous.comp","Continuous.norm","Continuous.pow","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DivInvMonoid.toDiv","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Equiv.Perm","EquivLike.toFunLike","EuclideanSpace","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.compactSupport_square_mul_log","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueFullMeasure_symmetric_compact_integral","GinibrePoincare.gueOrderedMeasure","GinibrePoincare.gueOrderedMeasure_square_lsi","GinibrePoincare.guePermute","GinibrePoincare.gueSymmetric_gradient_norm_sq","GinibrePoincare.squareEntropy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.fderiv","InnerProductSpace.toDual","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.continuous","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.instSemilinearIsometryEquivClass","LinearIsometryEquiv.symm","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Measurab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TNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff.of_le","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.trans","EuclideanSpace","False","Fin","Fin.fintype","GinibrePoincare.gueLSIWitness","GinibrePoincare.gueLSIWitness_contDiff","GinibrePoincare.gueLSIWitness_gradient_memLp","GinibrePoincare.gueLSIWitness_memLp","GinibrePoincare.gueLSIWitness_symmetric","GinibrePoincare.gueSymmetric_C1_pair_mem_H1Completion","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","Preorder.toLE","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","True","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_contDiff","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueLSIWitness","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instTopENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff.comp","ContDiff.div_const","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueCenterCoordinate","GinibrePoincare.gueCenterCoordinate_contDiff","GinibrePoincare.gueLSIWitness._proof_1","HDiv.hDiv","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.contDiff_exp","Real.denselyNormedField","Real.exp","Real.instDivInvMonoid","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","fact_one_le_two_ennreal","instHDiv","instOfNatAtLeastTwo","instOfNatNat","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_entropy_integral","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","GinibrePoincare.gueCenterVariance","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.log","Real.measurableSpace","Real.normedAddCommGroup","WithLp.measurableSpace","instHDiv","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","A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.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.mulAction","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PolynormableSpace.continuousSMul","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","RCLike.toStarRing","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAdd","Real.instAddCommGroup","Real.instCommSemiring","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.linearOrder","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SemilinearIsometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StrongDual","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instMulAction","WithLp.instSMul","Zero.toOfNat0","congr","congrArg","congrFun'","fact_one_le_two_ennreal","fderiv","funext","gradient","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","map_smul","rfl","smul_smul","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_gradient_energy","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueCenterVariance","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Se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iring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_one","norm_smul","rfl","sq_abs"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_gradient_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","fact_one_le_two_ennreal","gradient","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.continuous","Continuous","Continuous.aestronglyMeasurable","Continuous.div_const","Continuous.smul","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.mpr","Eq.refl","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.gueCenterUnit","GinibrePoincare.gueCenterVariance","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","GinibrePoincare.gueLSIWitness_contDiff","GinibrePoincare.gueLSIWitness_gradient","GinibrePoincare.gueLSIWitness_gradient_energy","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.of_integral_ne_zero","MeasureTheory.MemLp","MeasureTheory.integral","MeasureTheory.memLp_two_iff_integrable_sq_norm","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NNReal.toReal","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","PiLp.borelSpace","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.instPseudoEMetricSpace","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.secondCountableTopology","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.exp","Real.exp_pos","Real.instAddCommGroup","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instSMul","WithLp.measurableSpace","WithTop.some","Zero.toOfNat0","congrArg","continuous_const","div_pos","fact_one_le_two_ennreal","funext","gradient","id","instCountableFin","instHDiv","instHMul","instHPow","instHSMul","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instSecondCountableTopologyReal","instTopENat","mul_pos","ne_of_gt","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_lsi_equality","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.instNorm","PiLp.normedAddCommGroup","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","WithLp.measurableSpace","fact_one_le_two_ennreal","gradient","instHDiv","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gueCenterVariance","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","GinibrePoincare.gueLSIWitness_entropy_integral","GinibrePoincare.gueLSIWitness_gradient_energy","GinibrePoincare.gueLSIWitness_square_integral","GinibrePoincare.squareEntropy","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Inv.inv","InvOneClass.toInv","LT.lt","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.m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stDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","WithTop.some","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instCountableFin","instHDiv","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instTopENat","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_square","type_dependencies":["Eq","EuclideanSpace","Fin","GinibrePoincare.gueCenterCoordinate","GinibrePoincare.gueLSIWitness","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","OfNat.ofNat","Real","Real.exp","Real.instMonoid","instHPow","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","EuclideanSpace","Field.toSemifield","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gueCenterCoordinate","GinibrePoincare.gueLSIWitness","GinibrePoincare.gueLSIWitness._proof_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_add","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.instCommSemiring","Nat.mul","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Real","Real.exp","Real.exp_add","Real.instAdd","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRing","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","pow_two","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","name":"GinibrePoincare.gueLSIWitness_square_integral","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","GinibrePoincare.gueCenterVariance","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueLSIWitness","HDiv.hDiv","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Monoid.toNPow","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","WithLp.measurableSpace","instHDiv","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.i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lSpace","Zero.toOfNat0","instPolynormableSpace"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.gueLogBarrierDeriv","GinibrePoincare.gueLogBarrierDerivTwo","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt","HasDerivAt.add","HasDerivAt.div","HasDerivAt.div_const","HasDerivAt.sub_const","Inv.inv","LE.le","LT.lt","LT.lt.trans_le","Module","Module.toDistribMulAction","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.instDiv","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.decidableLE","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instLE","Real.instLT","Real.instMonoid","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceGUEBarrier.0.GinibrePoincare.hasDerivAt_splice","add_zero","congr","congrArg","congrFun'","eq_of_heq","eq_self","funext","hasDerivAt_const","hasDerivAt_id","heq_of_eq","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instPolynormableSpace","ite","mul_one","ne_of_gt","of_eq_true","one_div","sub_neg_eq_add","sub_self","zero_add","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEBarrier","name":"GinibrePoincare.gueLogBarrier_contDiff","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","GinibrePoincare.gueLogBarrier","LT.lt","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedField.toNormedSpace","OfNat.ofNat","Real","Real.denselyNormedField","Real.instLT","Real.instZero","Real.normedAddCommGroup","WithTop","WithTop.natCast","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AnalyticOn","AnalyticOnNhd","And","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","Continuous","ContinuousOn.div","ContinuousOn.pow","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivInvMonoid.toDiv","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.gueLogBarrier","GinibrePoincare.gueLogBarrierDeriv","GinibrePoincare.gueLogBarrierDerivTwo","GinibrePoincare.gueLogBarrierDeriv_hasDerivAt","GinibrePoincare.gueLogBarrier_hasDerivAt","HAdd.hAdd","HDiv.hDiv","HPow.hPow","HasDerivAt.deriv","HasDerivAt.differentiableAt","IsEmpty.forall_iff._simp_1"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eal.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.univ","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","convexOn_of_deriv2_nonneg","convex_univ","deriv","dite","div_pos","even_two_mul","funext","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHDiv","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","interior","ite","ite_eq_left","ite_eq_right","le_of_lt","pow_pos"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUERegularizedPotential","name":"GinibrePoincare.gueLogBarrier_exp_bound","type_dependencies":["GinibrePoincare.gueLogBarrier","HMul.hMul","HPow.hPow","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","OfNat.ofNat","Real","Real.exp","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instZero","Zero.toOfNat0","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Even.pow_nonneg","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gueLogBarrier","GinibrePoincare.gueLogBarrier._proof_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toIsOrderedRing","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.neg_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathli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care.gueLogBarrier._proof_1","GinibrePoincare.gueLogBarrier_exp_bound","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LE.le.trans","LT.lt","LT.lt.trans","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.decidableLE","Real.exp","Real.exp_add","Real.exp_log","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.log","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","abs_nonneg","abs_of_pos","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","dite","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","ite","ite_eq_right","le_of_lt","le_of_not_gt","lt_of_not_ge","mul_nonneg_of_nonpos_of_nonpos","neg_neg_of_pos","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEBarrier","name":"GinibrePoincare.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name":"GinibrePoincare.guePermute_mul","type_dependencies":["Eq","Equiv.Perm","Equiv.Perm.instMul","EuclideanSpace","Fin","GinibrePoincare.guePermute","HMul.hMul","Nat","Real","instHMul"],"value_dependencies":["Equiv.Perm","EuclideanSpace","Fin","GinibrePoincare.guePermute","Nat","Real","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEChamberIntegrals","name":"GinibrePoincare.guePermute_volume_preserving","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv.Perm","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.guePermute","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.MeasurePreserving","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instDivisionRing","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","fact_one_le_two_ennreal","instCountableFin","instOfNatAtLeastTwo","instSecondCountableTopologyReal","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv.Perm","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.guePermuteIsometry","InnerProductSpace.toNormedSpace","LinearIsometryEquiv.measurePreserving","MeasurableSpace.pi","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.borelSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instDivisionRing","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","WithLp.measurableSpace","fact_one_le_two_ennreal","instCountableFin","instOfNatAtLeastTwo","instSecondCountableTopologyReal"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceGUEConvexity","name":"GinibrePoincare.gueRawDensity","type_dependencies":["EuclideanSpace","Fin","Nat","Real"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Finset.prod","Finset.sum","Finset.univ","GinibrePoincare.gueEnergy._proof_1","GinibrePoincare.guePairs","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","OfNat.ofNat","PiLp.innerProductSpace._proof_1","Prod","Prod.fst","Prod.snd","Real","Real.exp","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instSub","WithLp.ofLp","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUECenterGeometry","name":"GinibrePoincare.gueRawDensity_center_factorization","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.gueCenterUnit","GinibrePoincare.gueRawDensity","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Inner.inner","InnerProductSpace.toInner","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NormedAddCommGroup.toS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ormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","WithLp","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.seminormedAddCommGroup","Real","Real.normedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","WithLp","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEProjection","name":"GinibrePoincare.gueRealProjectionLinear._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","GinibrePoincare.gueRealProjectionLinear._proof_2","Module.toDistribMulAction","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp","WithLp.instAddCommGroup","WithLp.instModule","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toSemifield","Fin","Fin.fintype","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instRCLike","Real.instRing","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","UniformSpace.toTopologicalSpace","WithLp","WithLp.instAddCommGroup","WithLp.instModule","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEProjection","name":"GinibrePoincare.gueRealProjectionLinear.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.module","ContinuousLinearMap.toLinearMap","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","EuclideanSpace","Field.toSemifield","Fin","Fin.instOfNat","GinibrePoincare.gueRealProjectionLinear","GinibrePoincare.gueRealProjectionLinear._proof_1","GinibrePoincare.gueRealProjectionLinear._proof_10","GinibrePoincare.gueRealProjectionLinear._proof_11","GinibrePoincare.gueRealProjectionLinear._proof_12","GinibrePoincare.gueRealProjectionLinear._proof_13","GinibrePoincare.gueRealProjectionLinear._proof_2","GinibrePoincare.gueRealProjectionLinear._proof_3","GinibrePoincare.gueRealProjectionLinear._proof_4","GinibrePoincare.gueRealProjectionLinear._proof_5","GinibrePoincare.gueRealProjectionLinear._proof_6","GinibrePoincare.gueRealProjectionLinear._proof_7","GinibrePoincare.gueRealProjectionLinear._proof_8","GinibrePoincare.gueRealProjectionLinear._proof_9","LinearEquiv","LinearEquiv.symm","LinearEquiv.toLinearMap","LinearMap","LinearMap.addCommMonoid","LinearMap.comp","LinearMap.module","LinearMap.pi","LinearMap.toContinuousLinearMap","Nat","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGro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al.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","id","instCommSemiringNNRat","nhds","normedAlgebraRat","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUERegularizedLimit","name":"GinibrePoincare.gueRegularizedPairWeight_bound","type_dependencies":["GinibrePoincare.gueLogBarrier","GinibrePoincare.gueRegularizationScale","HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","OfNat.ofNat","One.toOfNat1","Real","Real.exp","Real.instAdd","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.gueLogBarrier","GinibrePoincare.gueLogBarrier_exp_polynomial_bound","GinibrePoincare.gueRegularizationScale","GinibrePoincare.gueRegularizationScale_le_one","GinibrePoincare.gueRegularizationScale_pos","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.mul_eq","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","Real","Real.commRing","Real.exp","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrder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inibrePoincare.guePermute","GinibrePoincare.gueSmoothAverage","HMul.hMul","Inv.inv","Nat","Nat.cast","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","instDecidableEqFin","instHMul"],"value_dependencies":["Eq.refl","EuclideanSpace","Fin","GinibrePoincare.gueSmoothAverage","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESmoothAveraging","name":"GinibrePoincare.gueSmoothAverage_compact","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","GinibrePoincare.gueSmoothAverage","HasCompactSupport","Nat","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","EmptyCollection.emptyCollection","Eq","Eq.mpr","Equiv.Perm","Equiv.instFintype","EquivLike.toFunLike","EuclideanSpace","Fin","Fin.fintype","Finset","Finset.induction_on","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.sum","Finset.sum_insert","Finset.univ","Fintype.card","Fintype.decidableEqEquivFintype","Function.comp","GinibrePoincare.guePermute","GinibrePoincare.guePermuteIsometry","HAdd.hAdd","HasCompactSupport","HasCompactSupport.add","HasCompactSupport.comp_homeomorph","HasCompactSupport.mul_left","HasCompactSupport.zero","Homeomorph","Homeomorph.instEquivLike","Insert.insert","Inv.inv","LinearIsometryEquiv.toHomeomorph","Membership.mem","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instAddMonoid","Real.instInv","Real.instNatCast","Real.instZero","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithLp.instModule","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","funext","id","instDecidableEqFin","instHAdd","instMulZeroClassOfSemiring","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESmoothAveraging","name":"GinibrePoincare.gueSmoothAverage_contDiff","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.gueSmoothAverage","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instTopENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContDiff","ContDiff.comp","ContDiff.mul","ContDiff.sum","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Equiv.Perm","Equiv.instFintype","EuclideanSpace","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.guePermute","GinibrePoincare.guePermuteIsometry","InnerProductSpace.toNormedSpace","Inv.inv","LinearIsometryEquiv.contDiff","Membership.mem","Nat","Nat.cast","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCo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oincare.gueSobolevAverage._proof_5","GinibrePoincare.gueSobolevAverage._proof_6","GinibrePoincare.gueSobolevPermutation","GinibrePoincare.gueSobolevPermutation._proof_2","GinibrePoincare.gueSobolevPermutation._proof_4","GinibrePoincare.gueSobolevPermutation._proof_5","HSMul.hSMul","Inv.inv","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod.distribSMul","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instRing","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.measurableSpace","fact_one_le_two_ennreal","instDecidableEqFin","instHSMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","name":"GinibrePoincare.gueSobolevAverage._proof_1","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","name":"GinibrePoincare.gueSobolevAverage._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","GinibrePoincare.GUEFullSobolevPair._proof_1","GinibrePoincare.gueFullMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","instIsTopologicalAddGroupReal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","GinibrePoincare.GUEFullSobolevPair._proof_1","GinibrePoincare.gueFullMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.measurableSpace","instIsTopologicalAddGroupReal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","name":"GinibrePoincare.gueSobolevAverage._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.GUEFullSobolevPair._proof_2","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueFullSmoothPairs._proof_2","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.measurableSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.GUEFullSobolevPair._proof_2","GinibrePoincare.gueFullMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.measurableSpace","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.measurableSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","name":"GinibrePoincare.gueSobolevAverage._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.GUEFullGradientL2","GinibrePoincare.GUEFullSobolevPair._proof_1","GinibrePoincare.GUEFullSobolevPair._proof_2","GinibrePoincare.GUEFullValueL2","GinibrePoincare.GUEFullValueL2._proof_1","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueSobolevAverage._proof_1","GinibrePoincare.gueSobolevAverage._proof_2","GinibrePoincare.gueSobolevAverage._proof_3","GinibrePoincare.gueSobolevPermutation._proof_2","GinibrePoincare.gueSobolevPermutation._proof_4","GinibrePoincare.gueSobolevPermutation._proof_5","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.instSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instMonoid","Real.instRing","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","SMulCommClass","SMulZeroClass.toSMul","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.measurableSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroC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ient","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","name":"GinibrePoincare.gueSobolevAverage_maps_core","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.GUEFullGradientL2","GinibrePoincare.GUEFullSobolevPair","GinibrePoincare.GUEFullSobolevPair._proof_1","GinibrePoincare.GUEFullSobolevPair._proof_2","GinibrePoincare.GUEFullValueL2","GinibrePoincare.GUEFullValueL2._proof_1","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueFullSmoothPairs","GinibrePoincare.guePaperSmoothPairs","GinibrePoincare.gueSobolevAverage","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.instIsBoundedSMul","PiLp.normedAddCommGroup","PiLp.seminormedAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instRing","Real.isBoundedSMul","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set.MapsTo","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.measurableSpace","fact_one_le_two_ennreal","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","And.left","And.right","CommRing.toNonUnitalCommRing","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Equiv.Perm","EuclideanSpace","Exists.casesOn","Exists.intro","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.GUEFullGradientL2","GinibrePoincare.GUEFullSobolevPair","GinibrePoincare.GUEFullSobolevPair._proof_1","GinibrePoincare.GUEFullSobolevPair._proof_2","GinibrePoincare.GUEFullValueL2","GinibrePoincare.GUEFullValueL2._proof_1","GinibrePoincare.gueFullMeasure","GinibrePoincare.gueFullSmoothPairs","GinibrePoincare.gueFullSmoothPairs._proof_1","GinibrePoincare.gueFullSmoothPairs._proof_2","GinibrePoincare.gueFullSmoothPairs._proof_3","GinibrePoincare.guePaperSmoothPairs","GinibrePoincare.guePaperSmoothPairs._proof_1","GinibrePoincare.guePaperSmoothPairs._proof_2","GinibrePoincare.guePaperSmoothPairs._proof_3","GinibrePoincare.guePermute","GinibrePoincare.gueSmoothAverage","GinibrePoincare.gueSmoothAverage_compact","GinibrePoincare.gueSmoothAverage_contDiff","GinibrePoincare.gueSmoothAverage_symmetric","GinibrePoincare.gueSobolevAverage","GinibrePoincare.gueSobolevAverage_core","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","Measu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edAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","congrArg","congrFun'","continuous_const","fact_one_le_two_ennreal","fderiv","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instCountableFin","instHMul","instHPow","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","locallyCompact_of_proper","nhds","one_ne_zero","pow_two","tendsto_finsetSum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESpatialApproximation","name":"GinibrePoincare.gueSpatialTruncation_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSpatialTruncation","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithTop","WithTop.one","fact_one_le_two_ennreal","fderiv","instHAdd","instHMul","instOfNatAtLeastTwo","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Bool","Bool.false","CommMagma.toMul","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","EuclideanSpace","False","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSpatialCutoff_smooth","GinibrePoincare.gueSpatialTruncation","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.fderiv","HasFDerivAt.mul","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Metric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iring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Equiv.Perm","Equiv.instFintype","EuclideanSpace","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_const_zero","Finset.univ","Fintype.card","GinibrePoincare.guePermute","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSpatialCutoff_derivative_tendsto","GinibrePoincare.gueSymmetricSpatialCutoff","GinibrePoincare.gueSymmetricSpatialCutoff_fderiv","HMul.hMul","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Nat.cast","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.instRing","Real.instZero","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","Zero.toOfNat0","congrArg","congrFun'","fderiv","funext","id","instDecidableEqFin","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","nhds","tendsto_finsetSum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricCutoff","name":"GinibrePoincare.gueSymmetricSpatialCutoff_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv.Perm","Equiv.instFintype","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.guePermute","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSymmetricSpatialCutoff","HMul.hMul","Inv.inv","Nat","Nat.cast","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.instRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","fderiv","instDecidableEqFin","instHMul","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.differentiable","ContinuousLinearEquiv.hasFDerivAt","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.refl","Eq.trans","Equiv.Perm","Equiv.instFintype","EuclideanSpace","False","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Fintype.card","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.guePermute","GinibrePoincare.guePermuteIsometry","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSpatialCutoff_smooth","GinibrePoincare.gueSymmetricSpatialCutoff","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.const_mul","HasFDerivAt.fderiv","HasFDerivAt.fun_sum","InnerProductSpace.toNormedSpace","Inv.inv","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LinearIsometryEquiv.toContinuousLinearEquiv","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.cast","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.module","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","PiLp.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivisionRing","Real.instInv","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","SubNegMonoid.toAddMonoid","Top.top","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","fderiv","id","instDecidableEqFin","instDistribOfSemiring","instHMul","instHSMul","instIsTopologicalRingReal","instOfNatAtLeastTwo","instPolynormableSpace","instSMulOfMul","instTopENat","instZeroENat","not_false_eq_true","of_eq_true","smul_apply","sum_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricCutoff","name":"GinibrePoincare.gueSymmetricSpatialCutoff_mem_unit","type_dependencies":["And","EuclideanSpace","Fin","GinibrePoincare.gueSymmetricSpatialCutoff","LE.le","Nat","OfNat.ofNat","One.toOfNat1","Real","Real.instLE","Real.instOne","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And.intro","And.left","And.right","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Equiv.Perm","Equiv.inhabited'","Equiv.instFintype","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.sum_nonneg","Finset.univ","Fintype.card","Fintype.card_pos","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.guePermute","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSpatialCutoff_mem_unit"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CommGroup","Real.normedCommRing","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Top.top","WithLp.instModuleFinite","WithTop.some","contDiff_const","fact_one_le_two_ennreal","instDecidableEqFin","instOfNatAtLeastTwo","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricCutoff","name":"GinibrePoincare.gueSymmetricSpatialCutoff_symmetric","type_dependencies":["Eq","Equiv.Perm","EuclideanSpace","Fin","GinibrePoincare.guePermute","GinibrePoincare.gueSymmetricSpatialCutoff","Nat","Real"],"value_dependencies":["Eq","Eq.mpr","Eq.rec","Eq.refl","Equiv.Perm","Equiv.Perm.instMul","Equiv.Perm.permGroup","Equiv.instFintype","Equiv.mulLeft","Equiv.sum_comp","EuclideanSpace","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Fintype.card","GinibrePoincare.guePermute","GinibrePoincare.gueSpatialCutoff","GinibrePoincare.gueSymmetricSpatialCutoff","HMul","HMul.hMul","Inv.inv","Membership.mem","Nat","Nat.cast","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","SetLike.instMembership","congrArg","congrFun'","id","instDecidableEqFin","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricCutoff","name":"GinibrePoincare.gueSymmetricSpatialCutoff_tendsto","type_dependencies":["EuclideanSpace","Filter.Tendsto","Filter.atTop","Fin","GinibrePoincare.gueSymmetricSpatialCutoff","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Distrib.toMul","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv.Perm","Equiv.inhabited'","Equiv.instFintype","EuclideanSpace","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.atTop","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_const","Finset.univ","Fintype.card","Fintype.card_ne_zero","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.bakryBoundedSpatialCutoff","GinibrePoincare.guePermute","GinibrePoincare.gueSpatialCutoff_tendsto","GinibrePoincare.gueSymmetricSpatialCutoff","GroupWithZero.toMonoidWithZero","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NSMul.toSMul","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instPreorder","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.addCommGroup","Pi.module","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInv","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","WithLp.instModuleFinite","Zero.toOfNat0","cast","congrArg","fact_one_le_two_ennreal","id","instDecidableEqFin","instHMul","instHSMul","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","inv_mul_cancel\u2080","mul_one","nhds","nsmul_eq_mul","tendsto_finsetSum"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetri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roup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","congrArg","congrFun'","continuous_const","fact_one_le_two_ennreal","fderiv","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instCountableFin","instHMul","instHPow","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","locallyCompact_of_proper","nhds","one_ne_zero","pow_two","tendsto_finsetSum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUESymmetricSpatialApproximation","name":"GinibrePoincare.gueSymmetricSpatialTruncation_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","EuclideanSpace","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.gueSymmetricSpatialCutoff","GinibrePoincare.gueSymmetricSpatialTruncation","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithTop","WithTop.one","fact_one_le_two_ennreal","fderiv","instHAdd","instHMul","instOfNatAtLeastTwo","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Bool","Bool.false","CommMagma.toMul","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","EuclideanSpace","False","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.gueSymmetricSpatialCutoff","GinibrePoincare.gueSymmetricSpatialCutoff_smooth","GinibrePoincare.gueSymmetricSpatialTruncation","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.fderiv","HasFDerivAt.mul","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.cast_one",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CommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","Semifield.toCommSemiring","SemilinearIsometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SeparatelyContinuousMul.to_continuousSMul","Set","Set.instMembership","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","StrongDual","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","TopologicalSpace.SecondCountableTopology.to_separableSpace","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithLp.instAddCommGroup","WithLp.instModule","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.ofLp","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instPreorder","WithTop.instSemiring","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","abs","autoParam","closure","congr","congrArg","congrFun'","fact_one_le_two_ennreal","fderiv","funext","gradient","id","instAddENat","instAddMonoidWithOneENat","instArchimedeanNat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instCountableFin","instDecidableEqFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInhabitedNat","instIsDirectedOrder","instIsTopologicalRingReal","instLTNat","instLinearOrderENat","instNoZeroDivisorsENat","instNonemptyOfInhabited","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instSecondCountableTopologyReal","instTopENat","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","isClosed_closure","locallyCompact_of_proper","map_zero","nhds","not_false_eq_true","of_eq_true","smulCommClass_self","sq_abs","starRingEnd","subset_closure","tendsto_finsetSum","tendsto_iff_dist_tendsto_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceGUEProjection","name":"GinibrePoincare.gue_gradient_coordinate","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","EuclideanSpace.basisFun","Field.toSemifield","Fintype","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","OrthonormalBasis","OrthonormalBasis.instFunLike","Pi.Function.module","Pi.addCommGroup","PiLp.completeSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instModule","WithLp.ofLp","fact_one_le_two_ennreal","fderiv","gradient","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DecidableEq","DenselyNormedField.toNontriviallyNormedField","Dens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ro.toOfNat0","emetricSpacePi","instR1Space","subset_closure","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.hasCompactSupport_dbarComponent","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instNatCast","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HasCompactSupport","HasCompactSupport.add","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","MulZeroClass.toMul","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instAdd","Pi.instMul","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","id","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.hasCompactSupport_ginibreDirectionalFlux_core","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreLebesgueDensityReal","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","And","And.left","And.right","CommSemiring.toSemiring","Compl.compl","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.ginibreLebesgueDensityReal","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","LE.le","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instCompl","Set.instLE","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instTopENat","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGeneratorL2","name":"GinibrePoincare.hasCompactSupport_ginibrePregenerator","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibrePregenerator","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibrePregenerator","GinibrePoincare.ginibrePregenerator_eq_zero_of_notMem_tsupport","HasCompactSupport","HasCompactSupport.intro","Membership.mem","MetricSpace.toEMetricSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Not","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","TopologicalSpace.PseudoMetrizableSpace.regularSpace","UniformSpace.toTopologicalSpace","instR1Space","instR1SpaceForall","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.hasCompactSupport_normalizedVandermonde_ofReal","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Complex.ofReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.normalizedVandermondeTransform","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.ofReal","Eq","Eq.mpr","Fin","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.normalizedVandermondeTransform_apply","GinibrePoincare.vandermonde","HMul.hMul","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.mul_left","Inv.inv","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","eq_self","funext","id","instHMul","instMulZeroClassOfSemiring","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.hasCompactSupport_realGradientNormSq_of_core","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.realGradientNormSq","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.left","And.right","Classical.byContradiction","CommSemiring.toSemiring","Compl.compl","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.refl","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const_zero","Finset.univ","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.realGradientNormSq","HAdd.hAdd","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","IsCompact.of_isClosed_subset","LE.le","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instMonoid","Real.instMonoidWithZero","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instCompl","Set.instLE","Set.instMembership","SetLike.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","add_zero","closure_minimal","congr","congrArg","congrFun'","eq_self","fderiv","fderiv_of_notMem_tsupport","instHAdd","instHPow","instInnerProductSpaceRealComplex","instOfNatNat","instTopENat","isClosed_tsupport","not_false_eq_true","of_eq_true","tsupport","zero_apply","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.hasDerivAt_configurationFourierCharacter_line","type_dependencies":["Complex","Complex.I","Complex.addCommGroup","Complex.instMul","Complex.instNormedField","Complex.ofReal","DenselyNormedField.toNontriviallyNormedField","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","GinibrePoincare.realScaleConfiguration","HMul.hMul","HasDerivAt","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex","instPolynormableSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommSemigroup.toCommMagma","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.exp","Complex.hasDerivAt_exp","Complex.instAdd","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.ofReal","Complex.ofReal_mul","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","GinibrePoincare.configurationRealPairing_realScale","GinibrePoincare.realScaleConfiguration","HAdd.hAdd","HMul.hMul","HPow.hPow","HasDerivAt","HasDerivAt.comp","HasDerivAt.comp_ofReal","HasDerivAt.congr_simp","HasDerivAt.mul_const","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tacti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"theorem","module":"GinibrePoincare.Analysis.BlockMagnitudeGradient","name":"GinibrePoincare.hasFDerivAt_blockMagnitudes","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Fin","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockMagnitudeDerivative","GinibrePoincare.blockMagnitudes","HAdd.hAdd","HasFDerivAt","InnerProductSpace.toNormedSpace","LT.lt","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instLT","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","ContinuousLinearMap.proj","DFunLike.coe","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockCoordinateProjection","GinibrePoincare.blockCoordinateProjection._proof_1","GinibrePoincare.blockMagnitudeDerivative._proof_1","GinibrePoincare.blockMagnitudeDerivative._proof_2","GinibrePoincare.blockMagnitudeDerivative._proof_3","GinibrePoincare.blockMagnitudeDerivative._proof_4","GinibrePoincare.blockMagnitudes","GinibrePoincare.blockRadiusDerivative","GinibrePoincare.blockRadiusDerivative._proof_1","GinibrePoincare.blockRadiusDerivative._proof_2","GinibrePoincare.blockRadiusDerivative._proof_3","GinibrePoincare.blockRadiusDerivative._proof_4","GinibrePoincare.configurationNormSq","GinibrePoincare.gaussianBlockRadii","GinibrePoincare.hasFDerivAt_blockRadii","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.const_mul","HasFDerivAt.sqrt","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_eq_eval_of_eq_of_eq","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval"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Derivative","name":"GinibrePoincare.hasFDerivAt_holomorphicHermite_series","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","HMul.hMul","HasFDerivAt","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHMul","instLTNat","instOfNatNat","tsum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Bool","Bool.false","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.ofReal","ContDiff.differentiable_one","ContDiffAt.differentiableAt_one","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instSMul","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.topologicalSpace","Convex.isPreconnected","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.const_mul","Differentiable.fun_comp","Differentiable.fun_pow","DifferentiableAt","DifferentiableAt.const_mul","DifferentiableAt.fun_comp'","DifferentiableAt.fun_pow","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized_zero_right","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.norm_fderiv_holomorphicHermite_le","GinibrePoincare.summable_holomorphicHermite_series","GinibrePoincare.summable_tensor_holomorphicHermite_bound","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasFDerivAt","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","LE.le","LE.le.trans","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.N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":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticGradientTransfer","name":"GinibrePoincare.hasFDerivAt_potentialSquaredRadii","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.potentialSquaredRadii","GinibrePoincare.potentialSquaredRadiiDerivative","HasFDerivAt","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.comp","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","ContinuousLinearMap.proj","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.potentialSquaredRadii","GinibrePoincare.potentialSquaredRadiiDerivative._proof_1","GinibrePoincare.potentialSquaredRadiiDerivative._proof_2","GinibrePoincare.potentialSquaredRadiiDerivative._proof_3","GinibrePoincare.potentialSquaredRadiiDerivative._proof_4","GinibrePoincare.potentialSquaredRadiiDerivative._proof_5","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HasFDerivAt","HasFDerivAt.add","HasFDerivAt.comp","HasFDerivAt.mul","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Module","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.instAdd","Pi.instMul","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoEMetricSpace.toUniformSpace","Pse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roup.toAdd","Complex","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","DistribMulAction.toMulAction","Field.toDivisionRing","Fin","FormalMultilinearSeries","GinibrePoincare.Configuration","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.Function.module","Pi.addCommMonoid","Pi.continuousAdd'","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SemigroupAction.toSMul","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instContinuousConstSMulForall"],"value_dependencies":["CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","Complex.ofReal","ContinuousMultilinearMap","ContinuousMultilinearMap.addCommMonoid","ContinuousMultilinearMap.domDomCongr","ContinuousMultilinearMap.instSMul","Eq","Fin","Fin.fintype","Finset.prod","Finset.sum","Finset.univ","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.finite_holomorphic_degree_fiber","GinibrePoincare.holomorphicHermiteFormalSeries._proof_1","GinibrePoincare.holomorphicHermiteFormalSeries._proof_2","GinibrePoincare.holomorphicHermiteFormalSeries._proof_3","GinibrePoincare.holomorphicHermiteFormalSeries._proof_4","GinibrePoincare.holomorphicMonomialMultilinear","HMul.hMul","HSMul.hSMul","Membership.mem","Nat","Nat.instAddCommMonoid","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Set","Set.Elem","Set.Finite.fintype","Set.instMembership","Set.ofPred","Subtype.val","UniformSpace.toTopologicalSpace","finCongr","instHMul","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryHolomorphicFormalSeries","name":"GinibrePoincare.holomorphicHermiteFormalSeries._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryHolomorphicFormalSeries","name":"GinibrePoincare.holomorphicHermiteFormalSeries._proof_2","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousConstSMul","MulZeroClass.toMul","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudo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ilinear","GinibrePoincare.holomorphicMonomialMultilinear_norm_le","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsOrderedRing.toZeroLEOneClass","IsScalarTower.left","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Nat.factorial","Nat.factorial_pos","Nat.instAddCommMonoid","NeZero.charZero_one","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_normOneClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instCommMonoidWithZero","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_nonneg","Real.sqrt_pos_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Set","Set.Elem","Set.Finite.fintype","Set.Finite.toFinset","Set.instMembership","Set.mem_toFinset._simp_1","Set.ofPred","Set.toFinite_toFinset","Set.toFinset","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","congrFun'","finCongr","forall_congr","id","iff_self","implies_true","inferInstance","instHDiv","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instSMulCommClassOfIsScalarTower","mul_le_of_le_one_right","mul_nonneg","norm_mul","norm_nonneg","norm_prod","norm_smul","norm_sum_le","of_eq_true","pow_nonneg","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryHolomorphicFormalSeries","name":"GinibrePoincare.holomorphicHermiteFormalSeries_radius","type_dependencies":["Complex","Complex.instDenselyNormedField","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instTop","Eq","Fin","Fin.fintype","FormalMultilinearSeries.radius","GinibrePoincare.Configuration","GinibrePoincare.holomorphicHermiteFormalSeries","InnerProductSpace.toNormedSpace","LE.le","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.innerProductSpace","Real","Real.instLE","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommRing.t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ormalSeries","name":"GinibrePoincare.holomorphicHermiteFormalSeries_sum","type_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedField","Complex.instSemiring","DistribMulAction.toMulAction","Eq","Field.toDivisionRing","Fin","FormalMultilinearSeries.sum","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.holomorphicHermiteFormalSeries","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SemigroupAction.toSMul","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SeparatelyContinuousMul.to_continuousSMul","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instContinuousConstSMulForall","instHMul","instLTNat","instOfNatNat","tsum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedField","Complex.instSemiring","Complex.instT2Space","ContinuousMultilinearMap","ContinuousMultilinearMap.funLike","DFunLike.coe","DistribMulAction.toMulAction","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_subtype","Finset.univ","FormalMultilinearSeries.sum","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.finite_holomorphic_degree_fiber","GinibrePoincare.holomorphicHermiteFormalSeries","GinibrePoincare.holomorphicHermiteFormalSeries_diagonal","GinibrePoincare.summable_holomorphicHermite_series","HEq","HEq.refl","HMul.hMul","HasSum","HasSum.tsum_eq","HasSum.tsum_fiberwise","Iff","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","SemigroupAction.toSMul","SeminormedAddCommGroup.to_isUniformAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SeparatelyContinuousMul.to_continuousSMul","Set","Set.Elem","Set.Finite.fintype","Set.Finite.mem_toFinset._simp_1","Set.Finite.toFinset","Set.instMembership","Set.instSingletonSet","Set.ofPred","Set.preimage","SetLike.instMembership","Singleton.singleton","Subtype","Subtype.val","Summable","Summable.hasSum","SummationFilter","SummationFilter.instLeAtTopUnconditional","SummationFilter.instNeBotUnconditional","SummationFilter.unconditional","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_of_heq","forall_congr","funext","id","iff_self","implies_true","instContinuousConstSMulForall","instHMul","instLTNat","instOfNatNat","of_eq_true","tsum","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ommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.casesOn","And.intro","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsFiniteHomogeneousQuotientVector","GinibrePoincare.IsFiniteHomogeneousQuotientVector._proof_1","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.eval_finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.eval_polynomialVandermonde","GinibrePoincare.finiteHomogeneousQuotientL2","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial","GinibrePoincare.finiteZeroAntiholomorphicHermitePolynomial_support_expansion","GinibrePoincare.finiteZeroAntiholomorphicHermiteSum","GinibrePoincare.finiteZeroHermiteL2","GinibrePoincare.finiteZeroHermiteL2_mem_gaussianAlternating","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreConstantClosedSubspace._proof_1","GinibrePoincare.ginibreConstantClosedSubspace._proof_3","GinibrePoincare.ginibreConstantL2._proof_2","GinibrePoincare.ginibreConstantL2._proof_3","GinibrePoincare.ginibreConstantL2._proof_4","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.globalPhase","GinibrePoincare.holomorphicHermiteCoefficient","GinibrePoincare.holomorphicHermiteSupport","GinibrePoincare.homogeneous_alternating_polynomial_division","GinibrePoincare.isAlternating_homogeneousComponent","GinibrePoincare.polynomialVandermonde","GinibrePoincare.totalHolomorphicDegree","GinibrePoincare.totalHolomorphicDegree_eq_of_mem_holomorphicHermiteSupport","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.IsHomogeneous","MvPolynomial.eval","MvPolynomial.homogeneousComponent","MvPolynomial.homogeneousComponent_isHomogeneous","NPow.toPow","Nat","Nat.add_sub_of_le","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","Ne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toNonUnitalRingHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSubNat","map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oMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalIndependentInitial","name":"GinibrePoincare.independentInitialCenterPathSpace","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","MeasurableSpace","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","borel","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalIndependentInitial","name":"GinibrePoincare.independentInitialConfigurationPathBorel","type_dependencies":["BorelSpace","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.independentInitialConfigurationPathSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["BorelSpace.mk","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.independentInitialConfigurationPathSpace","MeasurableSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalIndependentInitial","name":"GinibrePoincare.independentInitialConfigurationPathSpace","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","borel","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.IndependentNoiseMixture","name":"GinibrePoincare.independentNoiseMixture_joint_law","type_dependencies":["Eq","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","Prod","Prod.instMeasurableSpace","Prod.mk","Prod.snd"],"value_dependencies":["And","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","Eq","Eq.mp","Eq.mpr","HMul.hMul","Measurable","Measurable.comp","Measurable.prodMk","MeasurableSet","MeasurableSet.prod","MeasurableSpace","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.ext_prod","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instSFiniteMap","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsFiniteMeasure","MeasureTheory.Measure.prod_apply","MeasureTheory.Measure.prod_prod","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.lintegral","MeasureTheory.lintegral_mul_const","Membership.mem","Prod","Prod.instMeasurableSpace","Prod.mk","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd","Set.ofPred","Set.preimage","congrArg","congrFun'","funext","id","instDistribOfSemiring","instHMul","measurable_measure_prodMk_left","measurable_prodMk_left","measurable_snd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.IndependentNoiseMixture","name":"GinibrePoincare.independen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qFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast_one","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMonoid","Nat.instNeZeroSucc","Nat.rawCast","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Real.instOne","Real.instRing","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Trans.trans","True","True.intro","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","eq_true","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTransEq","norm_pow","of_eq_true","one_mul","one_pow","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterExpansion","name":"GinibrePoincare.inner_gaussianAlternation_of_alternating","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.gaussianAlternationOperator","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodu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oidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instTop","Fact","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","OfNat.ofNat","Top.top","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instTop","ENNReal.ofNat_ne_top._simp_1","Eq","Eq.trans","Fact.mk","False","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Not","OfNat.ofNat","Top.top","True","True.intro","congrArg","eq_false","eq_true","instOfNatAtLeastTwo","instOfNatNat","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"GinibrePoincare.instFiniteDimensionalRealGaussianProductSpace","type_dependencies":["FiniteDimensional","GinibrePoincare.GaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.normedField"],"value_dependencies":["FiniteDimensional","GinibrePoincare.GaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","Nat","Nat.recAux","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.normedField","_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instFiniteDimensionalRealGaussianProductSpace._proof_1","_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instFiniteDimensionalRealGaussianProductSpace._proof_2"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"GinibrePoincare.instIsAddHaarMeasureGaussianProductSpaceGaussianProductHaar","type_dependencies":["AddCommGroup.toAddGroup","GinibrePoincare.GaussianProductSpace","GinibrePoincare.gaussianProductHaar","GinibrePoincare.instMeasurableSpaceGaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","MeasureTheory.Measure.IsAddHaarMeasure","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","GinibrePoincare.GaussianProductSpace","GinibrePoincare.gaussianProductHaar","GinibrePoincare.instMeasurableSpaceGaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","MeasureTheory.Measure.IsAddHaarMeasure","Nat","Nat.recAux","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instIsAddHaarMeasureGaussianProductSpaceGaussianProductHaar._proof_1","_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instIsAddHaarMeasureGaussianProductSpaceGaussianProductHaar._proof_2"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductDerivativeConvolution","name":"GinibrePoincare.instIsAddHaarMeasureProdComplexProdVolume_ginibrePoincare","type_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Prod","Prod.instAddGroup","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instTopologicalSpaceProd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContinuousAdd.measurableAdd","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.Measure.IsAddHaarMeasure.mk","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toI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ePoincare._proof_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticSeparatedConvolution","name":"GinibrePoincare.instVAddInvariantMeasureProdComplexVolume_ginibrePoincare_1","type_dependencies":["Complex","Complex.borelSpace","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","FiniteDimensional.rclike_to_real","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.VAddInvariantMeasure","Prod","Prod.instAdd","instInnerProductSpaceRealComplex","instVAddOfAdd","measureSpaceOfInnerProductSpace"],"value_dependencies":["_private.GinibrePoincare.Analysis.NonQuadraticSeparatedConvolution.0.GinibrePoincare.instVAddInvariantMeasureProdComplexVolume_ginibrePoincare_1._proof_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteDegreeOrder","name":"GinibrePoincare.instWellFoundedLTDegreeHermiteIndex","type_dependencies":["DistribLattice.toLattice","GinibrePoincare.DegreeHermiteIndex","GinibrePoincare.instLinearOrderDegreeHermiteIndex","Lattice.toSemilatticeInf","Nat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","WellFoundedLT","instDistribLatticeOfLinearOrder"],"value_dependencies":["DistribLattice.toLattice","GinibrePoincare.DegreeHermiteIndex","GinibrePoincare.degreeHermiteKey","InvImage.wf","LT.lt","Lattice.toSemilatticeInf","Lex","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.Lex","Prod.Lex.instLT","Prod.Lex.instWellFoundedLTLex","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLTNat","instWellFoundedLTNat","wellFounded_lt"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.integerConfiguration","type_dependencies":["GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instNatCast","Fin","Fin.val","Nat","Nat.cast"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.integerConfiguration.eq_1","type_dependencies":["Complex","Complex.instNatCast","Eq","Fin","Fin.val","GinibrePoincare.integerConfiguration","Nat","Nat.cast"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.integerConfiguration","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.integerConfiguration_collisionFree","type_dependencies":["GinibrePoincare.CollisionFree","GinibrePoincare.integerConfiguration","Nat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Complex","Complex.re","Eq","Eq.mp","Eq.refl","Fin","Fin.ext","Fin.val","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.integerConfiguration","Nat","Nat.cast_inj._simp_1","Real","Real.instFloorRing","Real.instRing","Real.linearOrder","Real.partialOrder","Ring.toAddGroupWithOne","Ring.toSemiring","cast","congrArg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianProductIntegral","name":"GinibrePoincare.integrable_and_integral_prod_coordinateFunctions_complexGaussianMeasure","type_dependencies":["And","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Eq","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["And.intro","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Eq","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.integrable_prod_coordinateFunctions_complexGaussianMeasure","GinibrePoincare.integral_prod_coordinateFunctions_complexGaussianMeasure","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.integrable_complexGaussian_fderiv_imag","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","GinibrePoincare.complexCoordinateGaussianProbability","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","ContDiff","ContDiff.continuous_fderiv","Continuous.clm_apply","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq.refl","Field.toSemifield","GinibrePoincare.integrable_complexGaussian_of_continuous_hasCompactSupport","HasCompactSupport","HasCompactSupport.fderiv_apply","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat","Nat.cast_one","Nat.cast_zero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","fderiv","instAddMonoidWithOneENat","instCharZeroENat","instInnerProductSpaceRealComplex","instOneENat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.integrable_complexGaussian_fderiv_real","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","GinibrePoincare.complexCoordinateGaussianProbability","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousEN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","ContinuousENorm.toENorm","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instOne","Exists","Exists.casesOn","Filter.Eventually.of_forall","Function.comp","HMul.hMul","Iff.mp","IsCompact.exists_bound_of_continuousOn","LE.le","Measurable","Measurable.aestronglyMeasurable","Measurable.comp","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.of_bound","MeasureTheory.ae","MeasureTheory.memLp_one_iff_integrable","Membership.mem","MetricSpace.toEMetricSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.continuous_mul_log","Real.instConditionallyCompleteLinearOrder","Real.instLE","Real.instMul","Real.instPreorder","Real.instZero","Real.log","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHMul","instOrderTopologyReal","instSecondCountableTopologyReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.integrable_mul_multivariateNormalized","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ENNReal","ENNReal.HolderConjugate.instTwoTwo","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.memLp_two_multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.memLp","MeasureTheory.MemLp.integrable_mul","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialIntegrability","name":"GinibrePoincare.integrable_mul_mvPolynomial_diagonalEval","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.complexCoordinateGaussianProbability","HMul.hMul","Matrix.vecCons","Matrix.vecEmpty","MeasureTheory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SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul"],"value_dependencies":["AddCommGroup.toAddGroup","BorelSpace.opensMeasurable","Complex","Complex.continuous_ofReal","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.ofReal","Continuous","Continuous.comp","Continuous.integrable_of_hasCompactSupport","Continuous.mul","Field.toDivisionRing","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.continuous_realCoordinateDensity","GinibrePoincare.realCoordinateDensity","HMul.hMul","HasCompactSupport","HasCompactSupport.mul_right","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instRCLike","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RealGaussianIntegrationByParts","name":"GinibrePoincare.integrable_mul_realCoordinateDensity_deriv","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Complex.instZero","Complex.ofReal","Continuous","GinibrePoincare.realCoordinateDensity","HMul.hMul","HasCompactSupport","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.instNatCast","Real.instNeg","Real.measureSpace","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.continuous_ofReal","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.ofReal","Continuous","Continuous.comp","Continuous.integrable_of_hasCompactSupport","Continuous.mul","Field.toDivisionRing","FiniteDimensional.rclike_to_real","GinibrePoincare.continuous_realCoordinateDensity","GinibrePoincare.realCoordinateDensity","HMul.hMul","HasCompactSupport","HasCompactSupport.mul_right","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.MeasureSpace.volume","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_const","continuous_id","id","instHMul","instIsAddHaarMeasureVolume","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RealGaussianIntegrationByParts","name":"GinibrePoincare.integrable_mul_realCoordinateDensity_of_integrable","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Complex.ofReal","GinibrePoincare.realCoordinateDensity","GinibrePoincare.realCoordinateGaussianProbability","HMul.hMul","LT.lt","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","Real.measureSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","Complex","Complex.continuous_ofReal","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.norm_real","Complex.ofReal","Continuous.aestronglyMeasurable","Continuous.comp","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mp","Eq.mpr","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.continuous_realCoordinateDensity","GinibrePoincare.realCoordinateDensity","GinibrePoincare.realCoordinateGaussianMeasure_eq_withDensity","GinibrePoincare.realCoordinateGaussianPDF_formula","GinibrePoincare.realCoordinateGaussianProbability","GinibrePoincare.realCoordinateVariance","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mp","Iff.mpr","Inv.inv","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.mul","MeasureTheory.Integrable","MeasureTheory.Integrable.congr","MeasureTheory.Integrable.norm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.ae","MeasureTheory.integrable_norm_iff","MeasureTheory.integrable_withDensity_iff","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","NeZero.charZero_one","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Pi.instMul","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","ProbabilityTheory.gaussianPDF","ProbabilityTheory.gaussianPDF_lt_top","ProbabilityTheory.measurable_gaussianPDF","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.exp","Real.exp_pos","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.norm","Real.normedCommRing","Real.partialOrder","Real.pi","Real.pi_pos","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Real.sqrt_pos_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs_of_nonneg","congrArg","div_pos","eq_self","id","inferInstance","instHDiv","instHMul","instHPow","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","inv_pos_of_pos","le_of_lt","mul_pos","norm_mul","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialIntegrability","name":"GinibrePoincare.integrable_mvPolynomial_diagonalEval","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.complexCoordinateGaussianProbability","Matrix.vecCons","Matrix.vecEmpty","MeasureTheory.Integrable","MeasureTheory.ProbabilityMeasure.toMeasure","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instOfNatNat","starRingEnd"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.coeff","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidAlgebra.nonAssocSemiring","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","Distrib.toMul","ENormedAddCommMonoid.toESeminormedAddCommMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Filter.Eventually.of_forall","Fin","Fin.fintype","Fin.instOfNat","Fin.prod_univ_two","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.sum","Finset.sum_congr","Finset.univ","Finsupp","Finsupp.instAddZeroClass","Finsupp.instFunLike","Finsupp.prod","Finsupp.prod_fintype","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.integrable_const_mul_pow_mul_conj_pow_complexCoordinateGaussianProbability","HMul.hMul","HPow.hPow","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","Matrix.cons_val_fin_one","Matrix.vecCons","Matrix.vecEmpty","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.congr","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.ae","MeasureTheory.integrable_finsetSum","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MvPolynomial","MvPolynomial.as_sum","MvPolynomial.eval","MvPolynomial.eval_monomial","MvPolynomial.eval_sum","MvPolynomial.monomial","MvPolynomial.support","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.succ","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RingHom","RingHom.id","RingHom.instFunLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun","congrFun'","eq_self","funext","id","instDistribOfSemiring","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatNat","of_eq_true","pow_zero","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.integrable_normSq_dbarCompo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iv","MeasurableEquiv.instEquivLike","MeasurableEquiv.symm","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure.pi","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instOfNatNat"],"value_dependencies":["Complex","Complex.im","Complex.instMul","Complex.instNormedField","Complex.instZero","Complex.ofReal","Continuous","GinibrePoincare.integrable_complexGaussian_im_mul","GinibrePoincare.integrable_piRealGaussian_comp_complexEquiv","HMul.hMul","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.integrable_piRealGaussian_re_mul","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Complex.instZero","Complex.measurableEquivPi","Complex.measurableSpace","Complex.ofReal","Complex.re","Continuous","DFunLike.coe","EquivLike.toFunLike","Fin","Fin.fintype","GinibrePoincare.realCoordinateGaussianProbability","HMul.hMul","HasCompactSupport","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableEquiv.symm","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure.pi","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.measurableSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instOfNatNat"],"value_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Complex.instZero","Complex.ofReal","Complex.re","Continuous","GinibrePoincare.integrable_complexGaussian_re_mul","GinibrePoincare.integrable_piRealGaussian_comp_complexEquiv","HMul.hMul","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.integrable_planarL2BumpIntegrand","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.normed","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.toContinuousAdd","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.to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Noetherian","IsTopologicalAddGroup.toContinuousAdd","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instIsFiniteMeasureOnCompactsProdVolumeOfSFinite","MeasureTheory.Measure.instIsLocallyFiniteMeasureProdVolumeOfSFinite","MeasureTheory.Measure.instIsOpenPosMeasureProdVolumeOfSFinite","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.IsNoetherian.finite","Module.toDistribMulAction","Module.toMulActionWithZero","MulActionWithZero.toSMulWithZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.smul'","PolynormableSpace.continuousSMul","Prod","Prod.borelSpace","Prod.instMeasurableSpace","Prod.instZero","Prod.normedAddCommGroup","Prod.normedSpace","Prod.opensMeasurableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instDivisionRing","Real.instMonoid","Real.instMonoidWithZero","Real.instRCLike","Real.instRing","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instHSMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsSimpleModule","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","isNoetherian_of_isNoetherianRing_of_finite","isNoetherian_prod","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialL2MollifierAverage","name":"GinibrePoincare.integrable_radialL2MollifierIntegrand","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.radialMollifierKernel","HSMul.hSMul","IsTopologicalAddGroup.toContinuousAdd","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGrou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Poincare.integrable_square_mul_log_ginibre","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HMul.hMul","HPow.hPow","HasCompactSupport","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instMul","Real.instZero","Real.log","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instHPow","instLTNat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous","Continuous.integrable_of_hasCompactSupport","EMetricSpace.toPseudoEMetricSpace","Fin","Fin.fintype","Finite.of_fintype","GinibrePoincare.Configuration","GinibrePoincare.compactSupport_square_mul_log","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","HMul.hMul","HPow.hPow","HasCompactSupport","LT.lt","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Monoid.toNPow","NPow.toPow","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.borelSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instMul","Real.instZero","Real.log","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","instCountableFin","instHMul","instHPow","instLTNat","instOfNatNat","instSigmaCompactSpaceForallOfFinite","locallyCompact_of_proper","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEquilibriumOrthogonality","name":"GinibrePoincare.integrable_sum_radius_product","type_dependencies":["Complex","Complex.instMul","Complex.instNormedField","Complex.measurableSpace","Continuous","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.ginibreMeasure","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","GinibrePoincare.standardComplexGaussianMeasure","HMul.hMul","LE.le","MeasurableSpace.pi","MeasureTheory.Integrable","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gammaMeasure","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.instOne","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLENat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","Continuous","Continuous.aestronglyMeasurable","Continuous.measurable","Decidable.byContradiction","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Field.toDivisionRing","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSum_ginibre_gaussian","GinibrePoincare.coordinateSum_pairwiseRadius_indepFun","GinibrePoincare.ginibreMeasure","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.pairwiseRadius","GinibrePoincare.recenteredGammaShape","GinibrePoincare.standardComplexGaussianMeasure","Iff.mp","InnerProductSpace.toNormedSpace","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Measurable.aemeasurable","Measurable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uousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","UniformSpace.toTopologicalSpace","instHMul","instHSub","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoid.toAddCommSemigroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.id","And","And.left","And.right","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.measurableSpace","ContDiff","Continuous","Continuous.aestronglyMeasurable","Continuous.bounded_above_of_compact_support","Continuous.comp","ContinuousAdd.measurableAdd","ContinuousAdd.measurableMul\u2082","ContinuousLinearMap.lsmul","ContinuousNeg.measurableNeg","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.trans","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierKernel","GinibrePoincare.radialMollifierKernel_properties","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasureTheory.Integrable","MeasureTheory.Integrable.convolution_integrand","MeasureTheory.Integrable.mul_bdd","MeasureTheory.IsAddLeftInvariant.isAddRightInvariant","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsAddRightInvariantForallVolumeOfMeasurableAddOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_const_mul","MeasureTheory.integral_integral_swap","MeasureTheory.integral_mul_const","MetricSpace.toEMetricSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toNorm","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNorm","OfNat.ofNat","One.toOfNat1","Pi.addGroup","Pi.instSub","Pi.measurableAdd\u2082","Pi.measurableNeg","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.opensMeasurableSpace","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instLE","Real.instMul","Real.instOne","Real.instRCLike","Real.instSemigroup","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","Semigroup.toMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","Top.top","Topolo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bleTopology.frechetUrysohnSpace","FrechetUrysohnSpace.to_sequentialSpace","GinibrePoincare.vectorSpectralPositiveFunctional","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.complexToReal","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.instCommSemiring","Real.instZero","Real.measurableSpace","Real.metricSpace","Real.normedField","Real.pseudoMetricSpace","RealRMK.integral_rieszMeasure","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.to_isUniformAddGroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.borelSpace","Subtype.instMeasurableSpace","Subtype.pseudoMetricSpace","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","TopologicalSpace.t2Space_of_metrizableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instPolynormableSpace","instProperSpaceReal","instT2SpaceSubtype","instTopologicalSpaceSubtype","locallyCompact_of_proper","proper_of_compact","spectrum","spectrum.instCompactSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AngularMoments","name":"GinibrePoincare.intervalIntegrable_angularMode","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","GinibrePoincare.angularMode","IntervalIntegrable","MeasureTheory.MeasureSpace.volume","Nat","Neg.neg","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toENormedAddMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.instNeg","Real.measureSpace","Real.pi","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.I","Complex.continuous_ofReal","Complex.instField","Complex.instIntCast","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.ofReal","Continuous","Continuous.cexp","Continuous.comp'","Continuous.const_mul","Continuous.intervalIntegrable","Field.toDivisionRing","GinibrePoincare.angularMode","HMul.hMul","HSub.hSub","Int","Int.cast","Int.instSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.MeasureSpace.volume","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","Real","Real.instNeg","Real.locallyFinite_volume","Real.measureSpace","Real.pi","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_mul_const","id","instHMul","instHSub","instNatCastInt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexDensityComparison","name":"GinibrePoincare.interval_second_derivative_maximum_principle","type_dependencies":["CommSemiring.toSemiring","ContinuousAt","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","LE.le","LT.lt","Membership.mem","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instLT","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","Set","Set.Icc","Set.Ioo","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","And.left","And.right","CommRing.toRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ContinuousAt","ContinuousOn","ContinuousOn.mono","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","False","Field.toSemifield","GinibrePoincare.local_min_second_derivative_nonneg","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Icc_mem_nhds","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact.exists_isMinOn","IsLocalMin","IsMinOn","IsMinOn.isLocalMin","LE.le","LE.le.eq_or_lt","LE.le.trans_lt","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NontriviallyNormedField.toNormedField","NormedField.toField","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.decidableLE","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instConditionallyCompleteLinearOrder","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instPreorder","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioo","Set.Ioo_subset_Icc_self","Set.instMembership","Set.left_mem_Icc","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","deriv","id","inferInstance","instClosedIicTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instMulZeroClassOfSemiring","instOrderTopologyReal","lt_of_not_ge","not_lt_of_ge","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUReversalWeight","name":"GinibrePoincare.invariant_measure_withDensity_of_invariant_weight","type_dependencies":["ENNReal","ENNReal.measurableSpace","Eq","Measurable","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.withDensity"],"value_dependencies":["Classical.propDecidable","DFunLike.coe","ENNReal","ENNReal.instZero","ENNReal.measurableSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","Measurable","Measurable.indicator","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.ext","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.lintegral","MeasureTheory.lintegral_indicator","MeasureTheory.lintegral_map","MeasureTheory.withDensity_apply","Membership.mem","Not","OfNat.ofNat","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instMembership","Set.mem_preimage._simp_1","Set.preimage","True","Zero.toOfNat0","congr","congrArg","dite","eq_false","eq_self","eq_true","funext","id","not_false_eq_true","of_eq_true"]},{"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odule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContinuousConstSMul.continuous_const_smul","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianPermutationL2","GinibrePoincare.permutationSign","HSMul.hSMul","Iff","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsClosed","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.continuous","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.ext","Set.iInter","Set.instMembership","Set.mem_iInter._simp_1","Set.ofPred","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","iff_self","instHSMul","instOfNatAtLeastTwo","instOfNatNat","isClosed_eq","isClosed_iInter","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireSpaceClosure","name":"GinibrePoincare.isClosed_gaussianEntireL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgrou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edRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.ext","Set.iUnion","Set.instMembership","Set.mem_iUnion","Set.ofPred","Set.preimage","Subtype","Subtype.mk","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","id","instInnerProductSpaceRealComplex","isOpen_iUnion"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.isRelPrime_X_sub_X_of_ordered_pairs_ne","type_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instRing","Fin","Finsupp","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","HSub.hSub","IsRelPrime","LT.lt","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","Prod","Prod.mk","Ring.toAddGroupWithOne","Semiring.toMonoid","SubNegMonoid.toSub","instHSub","instLTFin"],"value_dependencies":["AddCancelMonoid.toIsCancelAdd","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","CommMonoidWithZero.toMonoidWithZero","CommSemiring.toCommMonoidWithZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instCommSemiring","Complex.instField","Complex.instRing","Dvd.dvd","Eq","Eq.mpr","Field.toSemifield","Fin","Fin.instPartialOrder","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.not_dvd_X_sub_X_of_ordered_pairs_ne","GinibrePoincare.prime_X_sub_X","HSub.hSub","Irreducible.isRelPrime_iff_not_dvd","IsDomain.toIsCancelMulZero","IsRelPrime","LT.lt","LT.lt.ne","Monoid.toSemigroup","MonoidWithZero.toMonoid","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","MvPolynomial.instIsCancelMulZeroOfIsCancelAdd","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","Not","PartialOrder.toPreorder","Prime.irreducible","Prod","Prod.mk","Ring.toAddGroupWithOne","Semiring.toMonoid","SubNegMonoid.toSub","congrArg","id","instHSub","instIsDomain","instLTFin","propext","semigroupDvd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.isSymmetric_eval_of_polynomial","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","DFunLike.coe","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsSymmetric","GinibrePoincare.IsSymmetricConfigurationPolynomial","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring"],"value_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AlgHom","AlgHom.funLike","Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Eq.symm","Fin","Finsupp","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.eval_permuteConfigurationPolynomial","GinibrePoincare.permute","GinibrePoincare.permuteConfigurationPolynomial","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","congrArg","id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.isSymmetric_quotient_of_vandermonde_mul_alternating","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.instMul","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Fin","Finsupp","Finsupp.instAdd","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsSymmetricConfigurationPolynomial","GinibrePoincare.polynomialVandermonde","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","instHMul"],"value_dependencies":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCancelMonoid.toIsCancelAdd","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddGroup.toAddCancelMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toIntCast","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.algebra","AddMonoidAlgebra.instIsLeftCancelAddZeroOfIsCancelAddOfUniqueSums","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.nonUnitalSemiring","AddMonoidAlgebra.semiring","AddZero.toAdd","AddZeroClass.toAddZero","AlgHom","AlgHom.algHomClass","AlgHom.funLike","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","Algebra.id","Algebra.toModule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instIntCast","Complex.instNormedField","DFunLike.coe","Distrib.toMul","DivInvMonoid.toMonoid","Eq","Eq.mp","Eq.mpr","Eq.trans","Equiv.Perm","Equiv.Perm.permGroup","Equiv.Perm.sign","False","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.ParticlePermutation","GinibrePoincare.isAlternating_polynomialVandermonde","GinibrePoincare.permutationSign","GinibrePoincare.permuteConfigurationPolynomial","GinibrePoincare.polynomialVandermonde","GinibrePoincare.polynomialVandermonde_ne_zero","Group.toDivInvMonoid","HAdd.hAdd","HMul.hMul","Int","Int.cast","Int.cast_eq_zero._simp_1","Int.instMonoid","Int.instNontrivial","Int.instSemiring","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","IsRightCancelAdd.addRightStrictMono_of_addRightMono","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidHom","MonoidHom.id","MonoidHom.instFunLike","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","MvPolynomial","MvPolynomial.C","MvPolynomial.C_ne_zero","MvPolynomial.instNoZeroDivisors","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Ne","NegZeroClass.toZero","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalAlgSemiHomClass.toMulHomClass","NonUnitalSemiring.toSemigroupWithZero","NormMulClass.toNoZeroDivisors","NormedCommRing.toNormedRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","RingHom","RingHom.instFunLike","Semigroup.toMul","SemigroupWithZero.toSemigroup","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","True.intro","TwoUniqueSums.of_covariant_left","TwoUniqueSums.toUniqueSums","Units","Units.instMulOneClass","Units.ne_zero._simp_1","Units.val","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","eq_false","eq_true","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instIsDomain","instIsLeftCancelAddOfAddLeftReflectLE","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instOfNat","instUniqueSumsFinsupp","map_mul","mul_assoc","mul_left_cancel\u2080","mul_ne_zero","not_false","not_false_eq_true","of_eq_true","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","name":"GinibrePoincare.isometry_complexImagSlice","type_dependencies":["Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","GinibrePoincare.complexImagSlice","Isometry","MetricSpace.toEMetricSpace","NormedField.toMetricSpace","Real","Real.metricSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instCommSemiring","Complex.instMul","Complex.instNorm","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.instSub","Complex.norm_I","Complex.norm_real","Complex.ofReal","Complex.ofReal_sub","Dist.dist","Distrib.toAdd","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.complexImagSlice","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Isometry","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr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mensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Fintype","Function.eval","GinibrePoincare.scaledStandardGaussian","GinibrePoincare.scaledStandardGaussian_toPi","Iff.mpr","InnerProductSpace.toNormedSpace","Measurable.aemeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.MeasurePreserving.comp_hasLaw","MeasureTheory.measurePreserving_eval","NNReal","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.module","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","ProbabilityTheory.HasLaw","ProbabilityTheory.HasLaw.fun_comp","ProbabilityTheory.HasLaw.mk","ProbabilityTheory.gaussianReal","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun_iff_hasLaw_pi_pi","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.normedAddCommGroup","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","WithLp.instModuleFinite","WithLp.measurableSpace","WithLp.measurable_ofLp","WithLp.ofLp","Zero.toOfNat0","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteDimensionalItoActualPathRemainder","name":"GinibrePoincare.itoActualPathQuadraticSum","type_dependencies":["NNReal","Nat","NormedAddCommGroup","Real"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HPow.hPow","HSub.hSub","Monoid.toNPow","NNReal","NPow.toPow","Nat","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMonoid","SubNegMonoid.toSub","instAddNat","instHAdd","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoActualPathRemainder","name":"GinibrePoincare.itoActualPathRemainder_div_one_add_quadratic_tendsto","type_dependencies":["ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Filter.Tendsto","Filter.atTop","GinibrePoincare.itoActualPathQuadraticSum","GinibrePoincare.itoActualPathTaylorRemainderSum","HAdd.hAdd","HDiv.hDiv","InnerProductSpace.toNormedSpace","IsOpen","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","ProperSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instDivInvMonoid","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHAdd","instHDiv","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.casesOn","And.intro","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionSemiring.toGroupWithZero","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.eventually","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.is_lt","Fin.val","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_le_sum","Finset.sum_nonneg","Finset.univ","GT.gt","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_le_end","GinibrePoincare.itoActualPathQuadraticSum","GinibrePoincare.itoActualPathTaylorRemainderSum","GinibrePoincare.itoTaylorRemainder","GinibrePoincare.itoTaylorRemainder_uniform_compact_open","GinibrePoincare.itoUniformPathMesh","GinibrePoincare.itoUniformPathMesh_increment_le","GinibrePoincare.itoUniformPathMesh_tendsto","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact","IsCompact.image_of_continuousOn","IsOpen","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Metric.tendsto_nhds","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.le_of_lt","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNorm","NormedField.toNormedDivisionRing","NormedSpace","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","ProperSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.image","Set.instLE","Set.instMembership","Set.mem_image_of_mem","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","abs","abs_of_nonneg","bot_le","congrArg","congrFun'","dist_zero_right","div_le_iff\u2080","gt_mem_nhds","half_lt_self","half_pos","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instStarRingReal","instTransEq_1","instTransLE","le_of_not_gt","lt_of_not_ge","mul_le_mul_of_nonneg_left","neg_neg_of_pos","nhds","norm_div","norm_sum_le","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoActualPathRemainder","name":"GinibrePoincare.itoActualPathRemainder_div_quadratic_tendsto","type_dependencies":["ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Filter.Tendsto","Filter.atTop","GinibrePoincare.itoActualPathQuadraticSum","GinibrePoincare.itoActualPathTaylorRemainderSum","HDiv.hDiv","InnerProductSpace.toNormedSpace","IsOpen","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PartialOrder.toPreorder","ProperSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHDiv","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toMul","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionSemiring.toGroupWithZero","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","Exists","Exists.casesOn","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.eventually","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.is_lt","Fin.val","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_le_sum","Finset.sum_nonneg","Finset.univ","GT.gt","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_le_end","GinibrePoincare.itoActualPathQuadraticSum","GinibrePoincare.itoActualPathTaylorRemainderSum","GinibrePoincare.itoTaylorRemainder","GinibrePoincare.itoTaylorRemainder_uniform_compact_open","GinibrePoincare.itoUniformPathMesh","GinibrePoincare.itoUniformPathMesh_increment_le","GinibrePoincare.itoUniformPathMesh_tendsto","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IsCompact","IsCompact.image_of_continuousOn","IsOpen","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans_lt","LT.lt","Membership.mem","Metric.tendsto_nhds","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Nat.le_of_lt","Ne.symm","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNorm","NormedField.toNormedDivisionRing","NormedSpace","Not","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","ProperSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.decidableEq","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instStarOrderedRing","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.image","Set.instLE","Set.instMembership","Set.mem_image_of_mem","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","abs","abs_of_nonneg","bot_le","congrArg","congrFun'","dist_zero_right","dite","div_le_iff\u2080","div_zero","eq_true","gt_mem_nhds","half_lt_self","half_pos","id","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instStarRingReal","instTransEq_1","instTransLE","lt_of_le_of_ne","nhds","norm_div","norm_sum_le","norm_zero","of_eq_true","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoActualPathRemainder","name":"GinibrePoincare.itoActualPathRemainder_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoTaylorRemainder","HAdd.hAdd","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsOpen","LE.le","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PartialOrder.toPreorder","ProperSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instAddNat","instHAdd","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.casesOn","And.intro","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ContDiffOn","ContinuousOn","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.eventually","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.is_lt","Fin.val","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_le_sum","Finset.univ","GT.gt","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_le_end","GinibrePoincare.itoTaylorRemainder","GinibrePoincare.itoTaylorRemainder_uniform_compact_open","GinibrePoincare.itoUniformPathMesh","GinibrePoincare.itoUniformPathMesh_increment_le","GinibrePoincare.itoUniformPathMesh_tendsto","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsCompact","IsCompact.image_of_continuousOn","IsOpen","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans_lt","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Metric.tendsto_nhds","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.le_of_lt","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","ProperSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.image","Set.instLE","Set.instMembership","Set.mem_image_of_mem","Set.ofPred","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","bot_le","congrArg","dist_zero_right","div_mul_cancel\u2080","div_pos","gt_mem_nhds","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instTransEq_1","instTransLE","instTransLELT","lt_of_not_ge","mul_le_mul_of_nonneg_left","mul_lt_mul_of_pos_left","neg_neg_of_pos","nhds","norm_sum_le","rfl","sub_eq_zero_of_eq"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteDimensionalItoActualPathRemainder","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UnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun","congrFun'","differentiableAt_const","eq_self","fderiv","fderiv_clm_apply","fderiv_fun_const","id","if_true","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCharZeroENat","instCommSemiringENat","instCompleteLinearOrderENat","instDecidableEqFin","instDecidableTrue","instFintypeProd","instHAdd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instZeroENat","ite","ite_congr","ite_eq_right_of_eq_false","of_eq_true","one_ne_zero._simp_1","smulCommClass_self","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoConfiguration","name":"GinibrePoincare.itoConfigurationIncrement_expansion","type_dependencies":["Algebra.toSMul","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRCLike","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","Eq","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.configurationEuclideanLinearEquiv","GinibrePoincare.ginibreCoordinateDirection","HSMul.hSMul","InnerProductSpace.toNormedSpace","LinearEquiv","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","instFintypeProd","instHSMul","instInnerProductSpaceRealComplex","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommMonoid.toMonoid","Complex","Complex.I","Complex.addGroupWithOne","Complex.ext","Complex.im","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.ofReal","Complex.re","Complex.re_add_im","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Eq.trans","EquivLike.toFunLike","False","Field.toSemifield","Fin","Fin.fintype","Fin.instCommMonoid","Fin.instNeZeroHAddNatOfNat_mathlib_1","Fin.instNonUnitalCommRing","Fin.instOfNat","Fin.sum_univ_two","Finset","Finset.instSe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","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","True","UniformContinuousOn","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","abs_of_nonpos","addRightReflectLE_of_addLeftReflectLE","congr","congrArg","congrFun'","congr_arg\u2082","continuous_const","contravariant_lt_of_covariant_le","dist_eq_norm","div_lt_iff\u2080","div_one","div_pos","eq_self","funext","gt_mem_nhds","id","inferInstance","instAddNat","instCommSemiringNNRat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsCancelMulZero","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instIsUniformAddGroupReal","instLENat","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNat","instOfNatNat","instOrderTopologyReal","instStarRingReal","instTransEq","instTransEq_1","instTransLE","instTransLELT","intervalIntegral","intervalIntegral.integral_sub","intervalIntegral.norm_integral_le_of_norm_le_const","intervalIntegral.sum_integral_adjacent_intervals","le_rfl","lt_of_not_ge","mul_le_mul","mul_nonneg_of_nonpos_of_nonpos","mul_one","mul_one_div","ne_of_gt","neg_neg_of_pos","nhds","norm_nonneg","norm_sum_le","normedAlgebraRat","nsmul_eq_mul","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","sub_apply","sub_eq_zero_of_eq","sub_nonneg","sub_nonpos","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoDriftRiemann","name":"GinibrePoincare.itoContinuousScalarRiemann_fin_tendsto","type_dependencies":["ContinuousOn","DivInvMonoid.toDiv","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instPreorder","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instOfNatNat","intervalIntegral","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Continuous.continuousOn","ContinuousLinearMap","ContinuousLinearMap.continuousSMul","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.topologicalSpace","ContinuousOn","ContinuousOn.smul","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Filter","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_coe","GinibrePoincare.ginibreUniformTime","GinibrePoincare.ginibreUniformTime_increment","GinibrePoincare.itoContinuousOperatorDriftRiemann_fin_tendsto","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MeasureTheory.Measure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","MulZeroOneClass.toMulOneClass","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","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","Zero.toOfNat0","congrArg","congrFun'","eq_self","id","inf_of_le_right","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","le_max_left","min_eq_left","monotone_const","of_eq_true","zero_div","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinementGeometry","name":"GinibrePoincare.itoIntersection_end_eq_of_positive","type_dependencies":["Eq","LT.lt","Max.max","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toMin","SemilatticeSup.toMax"],"value_dependencies":["Iff.mp","LT.lt","LT.lt.le","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","Or","Or.resolve_left","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toMin","SemilatticeSup.toMax","lt_irrefl","lt_max_iff","max_eq_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinementGeometry","name":"GinibrePoincare.itoIntersection_mem_bounds","type_dependencies":["And","LE.le","LT.lt","Max.max","Membership.mem","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toMin","SemilatticeSup.toMax","Set","Set.Ioc","Set.instMembership"],"value_dependencies":["And","And.intro","And.left","And.right","Eq","Eq.mp","GinibrePoincare.itoIntersection_end_eq_of_positive","LE.le","LE.le.trans","LE.le.trans_lt","LT.lt","LT.lt.trans_le","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toMin","SemilatticeSup.toMax","Set","Set.Ioc","Set.instMembership","congrArg","le_max_left","le_max_right","min_le_left","min_le_right"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinement","name":"GinibrePoincare.itoIntervalClamp","type_dependencies":["NNReal"],"value_dependencies":["Max.max","Min.min","NNReal","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","SemilatticeInf.toMin","SemilatticeSup.toMax"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinement","name":"GinibrePoincare.itoIntervalClamp.eq_1","type_dependencies":["Eq","GinibrePoincare.itoIntervalClamp","Max.max","Min.min","NNReal","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","SemilatticeInf.toMin","SemilatticeSup.toMax"],"value_dependencies":["Eq.refl","GinibrePoincare.itoIntervalClamp","NNReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinement","name":"GinibrePoincare.itoIntervalClamp_increment_comm","type_dependencies":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","GinibrePoincare.itoIntervalClamp","HSub.hSub","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","SubNegMonoid.toSub","instHSub"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.symm","Eq.trans","GinibrePoincare.itoIntervalClamp","HSub.hSub","LE.le","LE.le.trans","LinearOrder.toDecidableLE","LinearOrder.toPartialOrder","Max.max","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeSup.toMax","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","True","Zero.toOfNat0","congr","congrArg","dite","eq_self","instHSub","le_of_not_ge","le_total","max_eq_left","max_eq_right","min_eq_left","min_eq_right","of_eq_true","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinement","name":"GinibrePoincare.itoIntervalClamp_increment_eq_intersection","type_dependencies":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","GinibrePoincare.itoIntervalClamp","HSub.hSub","LE.le","Max.max","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeSup.toMax","SubNegMonoid.toSub","instHSub"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.mpr","Eq.refl","Eq.trans","GinibrePoincare.itoIntervalClamp","HSub.hSub","LE.le","LE.le.trans","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toMin","LinearOrder.toPartialOrder","Max.max","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeSup.toMax","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","True","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_self","id","instHSub","le_min","le_of_not_ge","max_assoc","max_eq_left","max_eq_right","min_eq_left","min_eq_right","min_le_left","of_eq_true","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoIntervalRefinement","name":"GinibrePoincare.itoIntervalClamp_increment_sum","type_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","Finset.range","Finset.sum","GinibrePoincare.itoIntervalClamp","HAdd.hAdd","HSub.hSub","LE.le","NNReal","NNReal.instPartialOrder","NNReal.instZero","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SubNegMonoid.toSub","Zero.toOfNat0","instAddNat","instHAdd","instHSub","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","Eq.mpr","Eq.trans","Finset.range","Finset.sum","Finset.sum_range_sub","GinibrePoincare.itoIntervalClamp","HAdd.hAdd","HSub.hSub","LE.le","LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Max.max","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instSemilatticeSup","NNReal.instZero","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SubNegMonoid.toSub","True","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","id","inf_of_le_right","instAddNat","instHAdd","instHSub","instOfNatNat","max_eq_right","min_eq_left","of_eq_true","sup_of_le_left","zero_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoQuadraticControl","name":"GinibrePoincare.itoNorm_add_sq_le","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","OfNat.ofNat","Real","Real.instAdd","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","instHAdd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Function.swap","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","norm_add_le","norm_nonneg","rfl","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoConvergenceInMeasure","name":"GinibrePoincare.itoNormalizedDominatedError_tendstoInMeasure","type_dependencies":["And","DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.Eventually","Filter.Tendsto","Filter.atTop","HAdd.hAdd","HDiv.hDiv","LE.le","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instOne","Real.instZero","Real.metricSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","instHAdd","instHDiv","nhds"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.left","And.right","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter","Filter.Eventually","Filter.Eventually.mono","Filter.Tendsto","Filter.Tendsto.norm","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.itoNormalizedError_tendstoInMeasure","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","LT.lt.le","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MeasureTheory.ae_all_iff","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instCommSemiring","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNorm","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.metricSpace","Real.norm","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","abs","abs_nonneg","abs_of_nonneg","congr","congrArg","congrFun'","div_le_div_of_nonneg_left","funext","id","inferInstance","instCountableNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","le_of_not_gt","lt_of_not_ge","neg_neg_of_pos","nhds","norm_div","norm_zero","rfl","squeeze_zero_norm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoConvergenceInMeasure","name":"GinibrePoincare.itoNormalizedError_tendstoInMeasure","type_dependencies":["DivInvMonoid.toDiv","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","Filter.Eventually","Filter.Tendsto","Filter.atTop","HAdd.hAdd","HDiv.hDiv","LE.le","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.TendstoInMeasure","MeasureTheory.ae","MetricSpace.toEMetricSpace","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instOne","Real.instZero","Real.metricSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0",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ormSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHAdd","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalAddGroupReal","instOfNatAtLeastTwo","instOfNatNat","iteratedFDeriv"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.left","And.right","CommMonoid.toMonoid","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContinuousMultilinearMap","ContinuousMultilinearMap.funLike","ContinuousMultilinearMap.hasOpNorm","ContinuousMultilinearMap.hasOpNorm'","ContinuousMultilinearMap.instIsSubApplyForall","ContinuousMultilinearMap.instSub","ContinuousMultilinearMap.le_opNorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Even.pow_nonneg","Field.toSemifield","Fin","Fin.fintype","Fin.prod_univ_two","Finset.prod","Finset.univ","GinibrePoincare.itoDirectionalHessian","GinibrePoincare.itoTaylorRemainder","GinibrePoincare.itoTaylorRemainder_eq_integral","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toIsOrderedRing","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Max.max","MeasureTheory.MeasureSpace.volume","Membership.mem","Min.min","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedDivisionRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.measureSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semi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TNat","instMulNat","instOfNatNat"],"value_dependencies":["Fin","Fin.mk","Fin.val","GinibrePoincare.itoUniformCoarseIndex._proof_1","HDiv.hDiv","HMul.hMul","LT.lt","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinementPast","name":"GinibrePoincare.itoUniformCoarseIndex._proof_1","type_dependencies":["Fin","Fin.val","HDiv.hDiv","HMul.hMul","LT.lt","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["Fin","Fin.is_lt","Fin.val","HDiv.hDiv","HMul.hMul","Iff.mpr","LT.lt","Nat","Nat.div_lt_iff_lt_mul","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.FiniteDimensionalItoDriftVariation","name":"GinibrePoincare.itoUniformDriftIncrement","type_dependencies":["Fin","HAdd.hAdd","NNReal","Nat","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.normedField","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Fin","Fin.val","GinibrePoincare.ginibreUniformBrownianTime","HAdd.hAdd","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.toReal","Nat","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.measureSpace","Real.normedField","instAddNat","instHAdd","instOfNatNat","intervalIntegral"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticRestrictedDriftRiemann","name":"GinibrePoincare.itoUniformDriftIncrement.eq_1","type_dependencies":["Eq","Fin","Fin.val","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformDriftIncrement","HAdd.hAdd","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.toReal","Nat","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.measureSpace","Real.normedField","instAddNat","instHAdd","instOfNatNat","intervalIntegral"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.itoUniformDriftIncrement","HAdd.hAdd","NNReal","Nat","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.normedField","instAddNat","instHAdd","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoDriftVariation","name":"GinibrePoincare.itoUniformDriftIncrement_eq_volterra_difference","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","ContinuousOn","Eq","Fin","Fin.val","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformDriftIncrement","HAdd.hAdd","HSub.hSub","MeasureTheory.MeasureSpace.volume","NNReal","NNReal.toReal","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set.Icc","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instHSub","instOfNatNat","intervalIntegral"],"value_dependencies":["And.intro","And.left","And.right","ContinuousOn","ContinuousOn.intervalIntegrable_of_Icc","ContinuousOn.mono","Fin","Fin.is_lt","Fin.val","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_le_end","HAdd.hAdd","IntervalIntegrable","LE.le","LE.le.trans","MeasureTheory.MeasureSpace.volume","Membership.mem","NNReal","NNReal.coe_nonneg","NNReal.toReal","Nat","Nat.le_of_lt","Nat.succ_le_of_lt","NormedAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedSpace","OfNat.ofNat","Preorder.toLE","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.locallyFinite_volume","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instLENat","instOfNatNat","intervalIntegral.integral_interval_sub_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoDriftVariation","name":"GinibrePoincare.itoUniformDriftIncrement_norm_le","type_dependencies":["DivInvMonoid.toDiv","Fin","GinibrePoincare.itoUniformDriftIncrement","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","Membership.mem","NNReal","NNReal.toReal","Nat","Nat.cast","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Set","Set.Icc","Set.instMembership","Zero.toOf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formRefinement","name":"GinibrePoincare.itoUniformNNTime_coe","type_dependencies":["Eq","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformTime","NNReal","NNReal.toReal","Nat","Real"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","DivisionSemiring.toGroupWithZero","Field.toSemifield","GinibrePoincare.itoUniformTime","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.coe_nonneg","NNReal.toReal","Nat","Nat.cast","Nat.cast_nonneg'","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Real","Real.coe_toNNReal","Real.instAddCommMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","Zero.toOfNat0","div_nonneg","id","instHMul","instMulZeroClassOfSemiring","mul_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNTime_common_samples_mem","type_dependencies":["And","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LT.lt","Membership.mem","NNReal","NNReal.instPartialOrder","NNReal.instZero","Nat","Nat.instDiv","OfNat.ofNat","PartialOrder.toPreorder","Set","Set.Icc","Set.instMembership","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["And","And.intro","Eq.mp","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coarse_le_fine","GinibrePoincare.itoUniformNNTime_le_end","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","LE.le.trans","LT.lt","LT.lt.le","Membership.mem","NNReal","NNReal.instOrderBot","NNReal.instPartialOrder","NNReal.instZero","Nat","Nat.instDiv","Nat.instPreorder","Nat.mul_comm","Nat.mul_pos","Nat.succ_le_of_lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Set","Set.Icc","Set.instMembership","Zero.toOfNat0","bot_le","congrArg","instAddNat","instHAdd","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNTime_end","type_dependencies":["Eq","GinibrePoincare.itoUniformNNTime","LT.lt","NNReal","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.symm","Eq.trans","EuclideanDomain.toMulDivCancelClass","Field.toEuclideanDomain","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformTime","HDiv.hDiv","HMul.hMul","LT.lt","LT.lt.ne'","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Nat.instPreorder","Ne","Not","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.toNNReal","Real.toNNReal_coe","Ring.toAddGroupWithOne","Ring.toSemiring","Zero.toOfNat0","cast","congrArg","id","instHDiv","instHMul","instLTNat","instOfNatNat","mul_div_cancel_right\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNTime_eq_brownianTime","type_dependencies":["Eq","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","NNReal","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","DivInvMonoid.toDiv","Eq","Eq.trans","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.cast_add","Nat.cast_one","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRing","Real.toNNReal","Ring.toAddGroupWithOne","True","congrArg","congrFun'","eq_self","instAddNat","instHAdd","instHDiv","instHMul","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialDensity","name":"GinibrePoincare.itoUniformNNTime_eq_ginibreUniformBrownianTime","type_dependencies":["Eq","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","NNReal","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.trans","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_coe","GinibrePoincare.ginibreUniformTime","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coe","GinibrePoincare.itoUniformTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","NNReal","NNReal.coe_injective","NNReal.toReal","Nat","Nat.cast","Nat.cast_add","Nat.cast_one","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRing","Ring.toAddGroupWithOne","True","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHDiv","instHMul","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationGrid","name":"GinibrePoincare.itoUniformNNTime_exists_close","type_dependencies":["And","Dist.dist","DivInvMonoid.toDiv","Exists","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","Nat","Nat.cast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toDist","Real","Real.instDivInvMonoid","Real.instLE","Real.instNatCast","instHDiv","instLENat","instLTNat","instOfNatNat","instPseudoMetricSpaceNNReal"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toOrderedSub","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Bool","Bool.true","CharP.cast_eq_zero","CharP.ofCharZero","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Decidable.decide","Dist.dist","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.intro","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coe","GinibrePoincare.itoUniformTime","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","InvOneClass.toOne","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.nnreal_coe_pos","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.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lt","NNReal","NNReal.instPartialOrder","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instLENat","instLTNat","instOfNatNat"],"value_dependencies":["Eq.mp","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_end","GinibrePoincare.itoUniformNNTime_mono","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","congrArg","instLENat","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNTime_mono","type_dependencies":["GinibrePoincare.itoUniformNNTime","Monotone","NNReal","NNReal.instPartialOrder","Nat","Nat.instPreorder","PartialOrder.toPreorder"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivisionSemiring.toGroupWithZero","Eq.symm","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.itoUniformTime","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.coe_nonneg","NNReal.toReal","Nat","Nat.cast","Nat.cast_le._simp_1","Nat.cast_nonneg","Nat.instPreorder","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAddCommMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Real.toNNReal_mono","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","cast","div_le_div_of_nonneg_right","id","instHMul","instLENat","instMulZeroClassOfSemiring","mul_le_mul_of_nonneg_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNTime_two_coarse_dist_le","type_dependencies":["Dist.dist","DivInvMonoid.toDiv","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","LE.le","LT.lt","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instDiv","OfNat.ofNat","PseudoMetricSpace.toDist","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instNatCast","instHAdd","instHDiv","instLTNat","instOfNatNat","instPseudoMetricSpaceNNReal"],"value_dependencies":["Dist.dist","DivInvMonoid.toDiv","Eq.mp","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformNNTime_coarse_dist_le_step","HAdd.hAdd","HDiv.hDiv","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","LE.le","LE.le.trans","LT.lt","NNReal","NNReal.toReal","Nat","Nat.cast","Nat.instDiv","Nat.mul_comm","OfNat.ofNat","PseudoMetricSpace.toDist","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instIsOrderedAddMonoid","Real.instLE","Real.instNatCast","Real.instPreorder","add_le_add","congrArg","dist_comm","dist_triangle","instHAdd","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat","instPseudoMetricSpaceNNReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformChain","name":"GinibrePoincare.itoUniformNNTime_zero","type_dependencies":["Eq","GinibrePoincare.itoUniformNNTime","NNReal","NNReal.instZero","Nat","OfNat.ofNat","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CharP.cast_eq_zero","CharP.ofCharZero","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.itoUniformNNTime","GinibrePoincare.itoUniformTime","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","MonoidWithZero.toMulZeroOneClass","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMul","Real.instNatCast","Real.instRing","Real.linearOrder","Real.partialOrder","Real.semiring","Real.toNNReal","Real.toNNReal_zero","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","True","Zero.toOfNat0","congrArg","congrFun'","eq_self","instHDiv","instHMul","instMulZeroClassOfSemiring","instOfNatNat","of_eq_true","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoUniformRefinement","name":"GinibrePoincare.itoUniformNNWeightedSum_difference_common_grid","type_dependencies":["Eq","Finset.range","Finset.sum","GinibrePoincare.itoUniformNNTime","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LT.lt","NNReal","Nat","Nat.instDiv","OfNat.ofNat","Real","Real.instAddCommMonoid","Real.instMul","Real.instSub","instAddNat","instHAdd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up","AddGroup.toSubNegMonoid","Fin","Fin.fintype","Fin.val","Finset.le_sup'","Finset.mem_univ","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformPathMesh","HAdd.hAdd","HSub.hSub","LE.le","NNReal","Nat","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","OfNat.ofNat","Real","Real.instLE","Real.instSemilatticeSup","SubNegMonoid.toSub","id","instAddNat","instHAdd","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoPathMesh","name":"GinibrePoincare.itoUniformPathMesh_nonneg","type_dependencies":["GinibrePoincare.itoUniformPathMesh","LE.le","NNReal","Nat","NormedAddCommGroup","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Fin","Fin.fintype","Fin.instOfNat","Fin.val","Finset.le_sup'","Finset.mem_univ","Finset.univ","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.itoUniformPathMesh","HAdd.hAdd","HSub.hSub","LE.le.trans","NNReal","Nat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Real","Real.instPreorder","Real.instSemilatticeSup","Real.instZero","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SubNegMonoid.toSub","Zero.toOfNat0","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat","norm_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteDimensionalItoPathMesh","name":"GinibrePoincare.itoUniformPathMesh_tendsto","type_dependencies":["ContinuousOn","Filter.Tendsto","Filter.atTop","GinibrePoincare.itoUniformPathMesh","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","Nat","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Algebra.toModule","And","And.casesOn","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ContinuousOn","Dist.dist","Distrib.toAdd","DistribLattice.toLattice","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Exists","Exists.casesOn","Field.toSemifield","Filter","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.const_mul","Filter.Tendsto.eventually","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.instInhabited","Fin.is_lt","Fin.val","Finset","Finset.instSetLike","Finset.sup'","Finset.sup'_lt_iff","Finset.univ","Finset.univ_nonempty","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","GinibrePoincare.ginibreUniformBrownianTime","GinibrePoincare.ginibreUniformBrownianTime_coe","GinibrePoincare.ginibreUniformBrownianTime_le_end","GinibrePoincare.ginibreUniformBrownianTime_mono","GinibrePoincare.ginibreUniformTime","GinibrePoincare.ginibreUniformTime_increment","GinibrePoincare.itoUniformPathMesh","GinibrePoincare.itoUniformPathMesh_nonneg","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","IsCompact.uniformContinuousOn_of_continuous","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsScalarTower.nnrat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Membership.mem","Metric.tendsto_nhds","Metric.uniformContinuousOn_iff","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NNReal","NNReal.dist_eq","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","Nat","Nat.cast","Nat.instNeZeroSucc","Nat.instPreorder","Nat.le_of_lt","Nat.le_succ","Nat.succ_le_of_lt","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocC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"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltJointCanonicalPath","name":"GinibrePoincare.jointCanonicalPathBorel","type_dependencies":["BorelSpace","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.jointCanonicalPathMeasurable","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["BorelSpace.mk","CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","GinibrePoincare.jointCanonicalPathMeasurable","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralTiltJointCanonicalPath","name":"GinibrePoincare.jointCanonicalPathMeasurable","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","Fin","GinibrePoincare.Configuration","MeasurableSpace","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousMap","ContinuousMap.compactOpen","Fin","GinibrePoincare.Configuration","Membership.mem","NNReal","NNReal.toReal","Nat","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","borel","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.jointComplexDerivative","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","Fin","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.proj","ContinuousLinearMap.smulRight","DFunLike.coe","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.jointComplexDerivative._proof_1","GinibrePoincare.jointComplexDerivative._proof_2","GinibrePoincare.jointComplexDerivative._proof_3","GinibrePoincare.realCoordinateDirection","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.jointComplexDerivative._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.jointComplexDerivative._proof_2","type_dependencies":["Algebra.id","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Distrib.toMul","IsScalarTower","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","IsScalarTower.right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.jointComplexDerivative._proof_3","type_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Module.toDistribMulAction","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toDivisionRing","IsModuleTopology.toContinuousSMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Module.toDistribMulAction","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","name":"GinibrePoincare.jointComplexDerivative_restrictScalars","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Complex","Complex.I","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.restrictScalars","DFunLike.coe","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.jointComplexDerivative","GinibrePoincare.realCoordinateDirection","HMul.hMul","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","LinearMap.IsScalarTower.compatibleSMul","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.isScalarTower","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.to_isCommutative","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddSemigroup.to_isAssociative","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Bool","Bool.true","CommMagma.to_isCommutative","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.ofReal","Complex.re","Complex.re_add_im","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.proj","ContinuousLinearMap.restrictScalars","ContinuousLinearMap.smulRight","ContinuousLinearMap.sum_apply","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.rightDistribClass","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.configuration_real_basis_expansion","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.jointComplexDerivative","GinibrePoincare.jointComplexDerivative._proof_1","GinibrePoincare.jointComplexDerivative._proof_2","GinibrePoincare.jointComplexDerivative._proof_3","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsAddCommutative.is_comm","IsMulCommutative.is_comm","IsScalarTower.complexToReal","IsScalarTower.right","Lean.Data.AC.Context.eq_of_norm","Lean.Data.AC.Context.mk","Lean.Data.AC.Expr.op","Lean.Data.AC.Expr.var","Lean.Data.AC.Variable","Lean.Data.AC.Variable.mk","LinearMap.IsScalarTower.compatibleSMul","List.cons","List.nil","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","Nat","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Option.none","Option.some","PLift","PLift.up","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.instAdd","Pi.isScalarTower","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.ofReal","RCLike.real_smul_eq_coe_smul","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.to_isAssociative","SemigroupAction.toSMul","SemigroupWithZero.toSemigroup","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toAddHomClass","SemilinearMapClass.toMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Std.Commutative","Std.IdempotentOp","Std.LawfulIdentity","S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CommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.l2ProductBilinear._proof_1","GinibrePoincare.l2ProductBilinear._proof_10","GinibrePoincare.l2ProductBilinear._proof_2","GinibrePoincare.l2ProductBilinear._proof_3","GinibrePoincare.l2ProductBilinear._proof_5","GinibrePoincare.l2ProductBilinear._proof_6","GinibrePoincare.l2ProductBilinear._proof_7","GinibrePoincare.l2ProductVector","GinibrePoincare.l2ProductVector._proof_1","GinibrePoincare.l2ProductVector._proof_2","GinibrePoincare.l2ProductVector_add_right","GinibrePoincare.l2ProductVector_smul_right","LinearMap","LinearMap.addCommMonoid","LinearMap.mk","LinearMap.module","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SFinite","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2Product","name":"GinibrePoincare.l2ProductBilinear._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","GinibrePoincare.l2ProductVector","GinibrePoincare.l2ProductVector_add_right","GinibrePoincare.l2ProductVector_smul_right","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.addCommMonoid","LinearMap.mk","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SFinite","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocS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italNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.trans","Field.toDivisionRing","GinibrePoincare.l2ProductOperators_ext_on_pure","GinibrePoincare.l2ProductRightOperator","GinibrePoincare.l2ProductRightOperator_pure","GinibrePoincare.l2ProductVector","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SigmaFinite","MeasureTheory.instSFiniteOfSigmaFinite","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","True","UniformSpace.toTopologicalSpace","congr","congrArg","eq_self","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2TensorOperators","name":"GinibrePoincare.l2ProductRightOperator_id","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.id","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","GinibrePoincare.l2ProductRightOperator","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.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UnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","TensorProduct","TensorProduct.addCommMonoid","TensorProduct.instModule","TensorProduct.instNormedAddCommGroup","TensorProduct.mapL","TensorProduct.mapL_tmul","TensorProduct.tmul","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2TensorOperators","name":"GinibrePoincare.l2ProductRightOperator_selfadjoint","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.adjoint","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.l2ProductRightOperator","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SigmaFinite","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toSemiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","S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rePoincare.l2ProductVector._proof_2","LinearIsometry.mk","LinearMap","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SFinite","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","TensorProduct","TensorProduct.instModule","TensorProduct.instNormedAddCommGroup","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2Product","name":"GinibrePoincare.l2ProductTensorIsometry._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","GinibrePoincare.l2ProductTensorMap","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SFinite","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","TensorProduct","TensorProduct.instModule","TensorProduct.instNormedAddCommGroup","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAdd","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.mk","AddZeroClass.toAddZero","CommRing.toRing","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.re","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Field.toCommRing","Field.toDivisionRing","GinibrePoincare.l2ProductTensorMap","GinibrePoincare.l2ProductTensorMap_inner","HPow.hPow","Iff.mp","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsOrderedRing.toMulPosMono","IsSemitopologicalRing.toIsSemitopologicalS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inormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHSMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Function.comp","Function.hasSMul","GinibrePoincare.l2ProductVector","GinibrePoincare.l2ProductVector_coeFn","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.Measure.quasiMeasurePreserving_snd","MeasureTheory.SFinite","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2ProductDensity","name":"GinibrePoincare.l2Product_eq_zero_of_inner_pure_tensors","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","Complex","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","GinibrePoincare.l2ProductVector","Inner.inner","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.instSFiniteOfSigmaFinite","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Bool","Bool.true","Classical.propDecidable","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instT2Space","Complex.instZero","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.l2IndicatorVector","GinibrePoincare.l2ProductVector","GinibrePoincare.l2Product_indicator_rectangle","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSet","MeasurableSet.prod","MeasurableSet.univ","MeasurableSpace","MeasurableSpace.generateFrom","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Integrable.ae_eq_of_withDensity\u1d65_eq","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsFiniteMeasure.toSigmaFinite","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_zero","MeasureTheory.Lp.ext","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsFiniteMeasure","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity\u1d65","MeasureTheory.MemLp.integrable","MeasureTheory.VectorMeasure","MeasureTheory.VectorMeasure.ext_of_generateFrom","MeasureTheory.VectorMeasure.instFunLikeSet","MeasureTheory.VectorMeasure.instIsZeroApplySet","MeasureTheory.VectorMeasure.instZero","MeasureTheory.VectorMeasure.zero_apply","MeasureTheory.ae","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integrable_zero","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_indicator","MeasureTheory.setIntegral_univ","MeasureTheory.withDensity\u1d65_apply","MeasureTheory.withDensity\u1d65_zero","Membership.mem","MonoidHomClass.toOneHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MonoidWithZeroHomClass.toZeroHomClass","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonAssocSemiring.toMulZeroOneClass","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedFiel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NegMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddZeroClass","AddZeroClass.toAddZero","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","EquivLike.toFunLike","Exists.intro","Function.comp","InnerProductSpace.toNormedSpace","IsTopologicalAddGroup.toContinuousAdd","LinearIsometry","LinearIsometry.instFunLike","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableEquiv.symm","MeasurableEquiv.symm_apply_apply","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.compMeasurePreserving.congr_simp","MeasureTheory.Lp.compMeasurePreserving_comp_apply","MeasureTheory.Lp.compMeasurePreserving_id_apply","MeasureTheory.Lp.compMeasurePreserving\u2097\u1d62","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.comp","MeasureTheory.MeasurePreserving.symm","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","funext","id","instOfNatAtLeastTwo","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2PiOperators","name":"GinibrePoincare.l2PullbackEquiv._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2PiOperators","name":"GinibrePoincare.l2PullbackEquiv._proof_3","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticL2PiOperators","name":"GinibrePoincare.l2PullbackEquiv._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRi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.Analysis.LebesgueL2Mollification","name":"GinibrePoincare.lebesgueL2BumpAverage._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toModule","Real","Real.normedField","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toIsBoundedSMul","Real","Real.normedField"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LebesgueL2Mollification","name":"GinibrePoincare.lebesgueL2BumpAverage._proof_4","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Fin","Fin.fintype","GinibrePoincare.Configuration","HasContDiffBump","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LebesgueL2Convolution","name":"GinibrePoincare.lebesgueL2BumpAverage_convolution_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.normed","ContinuousENorm.toENorm","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Filter.EventuallyEq","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.lebesgueL2BumpAverage","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.convolution","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.norme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MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.instSub","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toAdd","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","ContinuousAdd.measurableAdd","DFunLike.coe","DomAddAct","DomAddAct.instVAddSubtypeAEEqFunMemAddAddSubgroupLp","DomAddAct.mk","DomAddAct.vadd_Lp_ae_eq","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_apply","EquivLike.toFunLike","Field.toDivisionRing","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.lebesgueL2Translate._proof_1","GinibrePoincare.lebesgueL2Translate._proof_2","GinibrePoincare.lebesgueL2Translate._proof_3","GinibrePoincare.lebesgueL2Translate._proof_4","HAdd.hAdd","HSub.hSub","HVAdd.hVAdd","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableVAdd.toMeasurableConstVAdd","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddLeftInvariant.vaddInvariantMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.Pi.isAddLeftInvariant_volume","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.addCommMagma","Pi.instAdd","Pi.instNeg","Pi.instSub","Pi.measurableAdd","Pi.subNegMonoid","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","Subtype","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","add_comm","congrArg","congrFun'","id","instHAdd","instHSub","instHVAdd","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instSeparatelyContinuousAddOfContinuousAdd","instVAddOfAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableVAdd_of_add","measureSpaceOfInnerProductSpace","secondCountable_of_proper","sub_eq_add_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LebesgueL2MollificationMaps","name":"GinibrePoincare.lebesgueL2Translate_map","type_dependencies":["AddCommGroup.t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uous.comp","Continuous.comp'","Continuous.fun_pow","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_mul","ENNReal.ofReal_natCast","Eq","Eq.mpr","Eq.symm","Eq.trans","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.continuous_vandermonde","GinibrePoincare.integrable_vandermondeWeight_complexGaussianMeasure","GinibrePoincare.integral_radial_vandermonde_eq_factorial","GinibrePoincare.kostlanWeight","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermondeWeight_nonneg","HMul.hMul","HPow.hPow","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.lintegral","MeasureTheory.ofReal_integral_eq_lintegral_ofReal","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Nat.factorial","Nat.factorial_pos","NeZero.charZero_one","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommMonoid","Real.instCommMonoid","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.NonQuadraticKostlan.0.GinibrePoincare.bounded_radial_weight_integrable","_private.GinibrePoincare.Analysis.NonQuadraticKostlan.0.GinibrePoincare.integrable_kostlanWeight'","_private.GinibrePoincare.Analysis.NonQuadraticKostlan.0.GinibrePoincare.kostlanWeight_nonneg'","congrArg","congrFun'","continuous_apply","continuous_finsetProd","continuous_id'","eq_self","id","instDistribOfSemiring","instHMul","instHPow","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","le_of_lt","mul_nonneg","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BlockMagnitudeLift","name":"GinibrePoincare.lipschitz_blockMagnitudes","type_dependencies":["Complex","Complex.instNormedField","EMetricSpace.toPseudoEMetricSpace","Exists","Fin","Fin.fintype","Fin.val","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockMagnitudes","HAdd.hAdd","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","Nat","NormedField.toMetricSpace","OfNat.ofNat","Real","Real.metricSpace","instAddNat","instHAdd","instOfNatNat","pseudoEMetricSpacePi"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNorm","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.lipschitz","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Dist.dist","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.symm","EuclideanSpace","Exists.intro","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset.le_sup","Finset.mem_univ","Finset.sup","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.GaussianRadialBlocks","GinibrePoincare.blockMagnitudes","GinibrePoincare.gaussianBlockMagnitude","GinibrePoincare.gaussianBlockMagni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pport"],"value_dependencies":["ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.mpr","Eq.refl","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent_zero_of_notMem_tsupport","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","LE.le.trans","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Metric.ball","Metric.ball_subset_closedBall","Metric.closedBall","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.indicator","Set.indicator_of_mem","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congr","congrArg","dite","funext","id","instHMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instTopENat","measureSpaceOfInnerProductSpace","pseudoMetricSpacePi","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeault","name":"GinibrePoincare.localDolbeault_locallyL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dolbeaultOrdinaryL2","GinibrePoincare.dolbeaultOrdinaryL2._proof_1","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","IsCompact","IsOpen","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopENat","measureSpaceOfInnerProductSpace","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Bool","Bool.false","BorelSpa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iring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","even_two_mul","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","le_of_lt","le_of_not_gt","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","neg_neg_of_pos","rfl","secondCountable_of_proper","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightLocal","name":"GinibrePoincare.locallyIntegrable_of_positive_compact_weight","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","Exists","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","IsCompact","LE.le","LT.lt","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","And","And.casesOn","Bool","Bool.true","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instT2Space","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","Eq","Eq.mpr","Eq.refl","Exists","Exists.casesOn","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.rclike_to_real","Function.locallyCompactSpace_of_finite","GinibrePoincare.Configuration","GinibrePoincare.memLp_restrict_of_weight_lower_bound","IsCompact","IsCompact.measurableSet","IsCompact.measure_lt_top","LE.le","LT.lt","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.IntegrableOn","MeasureTheory.IsFiniteMeasure.mk","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsFiniteMeasureOnCompactsForallVolumeOfSigmaFinite","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_apply_univ","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable","MeasureTheory.locallyIntegrable_iff","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.t2Space","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real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ivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","Nat","Prod","Prod.fst","Prod.mk","Prod.mk.eta","Prod.snd","True","congrArg","congrFun'","eq_self","funext","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","name":"GinibrePoincare.matrixComplexEntryEquiv._proof_2","type_dependencies":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","Nat","Prod","Prod.fst","Prod.mk","Prod.snd"],"value_dependencies":["Complex","DFunLike.coe","Eq","Eq.trans","Equiv","Equiv.apply_symm_apply","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","Nat","Prod","Prod.fst","Prod.mk","Prod.snd","True","congr","congrArg","congrFun'","eq_self","funext","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","name":"GinibrePoincare.matrixComplexEntryEquiv._proof_3","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous","DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_apply","continuous_pi","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","name":"GinibrePoincare.matrixComplexEntryEquiv._proof_4","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous.comp'","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.MatrixRealSpace","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_apply","continuous_pi","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","name":"GinibrePoincare.matrixComplexEntryEquiv._proof_5","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Complex","Complex.instAddCommMonoid","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","HAdd.hAdd","Nat","Pi.addCommMonoid","Prod","Prod.mk","instHAdd"],"value_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Complex","Complex.instAddCommMonoid","DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","HAdd.hAdd","Nat","Pi.addCommMonoid","Prod","Prod.mk","instHAdd","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","name":"GinibrePoincare.matrixComplexEntryEquiv._proof_6","type_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","HSMul.hSMul","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.mk","Real","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroCl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ormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submonoid","Submonoid.instSetLike","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.MatrixUnitaryFlagSaturation.0.GinibrePoincare.matrixDiagonalPhase_unitary._simp_1_1","congrArg","congrFun'","instDecidableEqFin","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instTopologicalSpaceMatrix","map_zero","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurAtlasCover","name":"GinibrePoincare.matrixDiagonalUnitary_schur_preserves","type_dependencies":["AddCommMonoid.toAddMonoid","And","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Complex.instZero","Eq","Fin","Fin.fintype","HMul.hMul","InvolutiveStar.toStar","LT.lt","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","OfNat.ofNat","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","Zero.toOfNat0","instDecidableEqFin","instLTFin","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And.intro","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","HAdd.hAdd","HMul.hMul","HPow.hPow","Iff.mp","InvolutiveStar.toStar","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Matrix","Matrix.conjTranspose","Matrix.diagonal","Matrix.diagonal_apply_eq","Matrix.diagonal_apply_ne","Matrix.diagonal_conjTranspose","Matrix.diagonal_mul","Matrix.ext","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instStar","Matrix.mem_unitaryGroup_iff","Matrix.mul_diagonal","Matrix.one","Matrix.one_apply_eq","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","NormedField.toField","Not","OfNat.ofNat","One.toOfNat1","Pi.instStarForall","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","Trans.trans","True","Zero.toOfNat0","congr","congrArg","congrFun'","dite","eq_false","eq_self","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instLTFin","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instTransEq","mul_one","not_false_eq_true","of_eq_true","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixLocalSpectrum","name":"GinibrePoincare.matrixEigenbasis_eigenvalue_isRoot","type_dependencies":["CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instSemiring"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ivLike.toFunLike","Fin","Fin.fintype","Function.Injective","Function.hasSMul","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixBasisLeftVector","GinibrePoincare.matrixEigenvalueProjector","GinibrePoincare.matrixRankOneProjector","HSMul.hSMul","Matrix","Matrix.charpoly","Matrix.mulVec","Matrix.of","Module.Basis","Module.Basis.instFunLike","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Polynomial.Separable","Polynomial.eval","Semiring.toModule","Zero.toOfNat0","instDecidableEqFin","instHSMul","instSMulOfMul"],"value_dependencies":["And","And.casesOn","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instOne","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq","Eq.mp","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Function.Injective","Function.hasSMul","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixBasisLeftVector","GinibrePoincare.matrixBasis_twoSided_eigenmatrix","GinibrePoincare.matrixEigenvalueProjector","GinibrePoincare.matrixEigenvalueProjector_eigenmatrix","GinibrePoincare.matrixEigenvalueProjector_trace","GinibrePoincare.matrixRankOneProjector","HMul.hMul","HSMul.hSMul","Matrix","Matrix.charpoly","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.mulAction","Matrix.mulVec","Matrix.of","Matrix.smul","Matrix.trace","Module.Basis","Module.Basis.instFunLike","Monoid.toMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Polynomial.Separable","Polynomial.eval","Semiring.toModule","Semiring.toMonoid","Zero.toOfNat0","congrArg","congrFun'","instDecidableEqFin","instHSMul","instSMulOfMul","one_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralProjector","name":"GinibrePoincare.matrixEigenvalueProjector_mul","type_dependencies":["CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Function.Injective","Function.hasSMul","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixEigenvalueProjector","HMul.hMul","HSMul.hSMul","Matrix","Matrix.charpoly","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.mulVec","Matrix.of","Matrix.zero","Module.Basis","Module.Basis.instFunLike","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Polynomial.Separable","Polynomial.eval","Semiring.toModule","Zero.toOfNat0","instDecidableEqFin","instHSMul","instSMulOfMul","ite"],"value_dependencies":["CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Function.Injective","Function.hasSMul","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixBasisLeftVector","GinibrePoincare.matrixBasisLeftVector_biorthogonal","GinibrePoincare.matrixEigenvalueProjector","GinibrePoincare.matrixEigenvalueProjector_eq_rankOne","GinibrePoincare.matrixRankOneProjector","GinibrePoincare.matrixRankOneProjector_biorthogonal","HMul.hMul","HSMul.hSMul","Matrix","Matrix.charpoly","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.mulVec","Matrix.of","Matrix.zero","Module.Basis","Module.Basis.instFunLike","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Polynomial.Separable","Polynomial.eval","Semiring.toModule","Zero.toOfNat0","congr","congrArg","id","instDecidableEqFin","instHSMul","instSMulOfMul","ite","ite_congr"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixOverlapLowerBound","name":"GinibrePoincare.matrixEigenvalueProjector_overlap_ge","type_dependencies":["Complex","Complex.commRing","Complex.instCommSemiring","Complex.instSemiring","Complex.normSq","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixEigenvalueProjector","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iring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.ofLp","fderiv","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.measurableSpace","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixComplexEntryEquiv_gaussian_preserving","GinibrePoincare.matrixEntryFullSpectralLift","GinibrePoincare.matrixEntryFullSpectralLift_derivative_eq_simple","GinibrePoincare.matrixEntryGaussianMeasure","GinibrePoincare.matrixEntryIntrinsicSpectralGradient","GinibrePoincare.matrixGaussianMeasure","GinibrePoincare.matrixGaussian_charpoly_separable_ae","InnerProductSpace.toNormedSpace","LT.lt","Matrix.charpoly","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","Polynomial.Separable","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","WithLp.ofLp","fderiv","id","instCommCStarAlgebraComplex","instDecidableEqFin","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralLiftFullEntry","name":"GinibrePoincare.matrixEntryFullSpectralLift_derivative_eq_simple","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixEntryFullSpectralLift","GinibrePoincare.matrixEntryIntrinsicSpectralGradient","InnerProductSpace.toNormedSpace","Matrix","Matrix.charpoly","Matrix.of","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","Polynomial.Separable","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.ofLp","fderiv","instCommCStarAlgebraComplex","instDecidableEqFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.hasFDerivAt","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq.fderiv_eq","Fin","Fin.fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.MatrixRealIndex","GinibrePoincare.MatrixRealSpace","GinibrePoincare.ginibreCoordinateDirection","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixComplexEntryEquiv_direction","GinibrePoincare.matrixEntryFullSpectralLift","GinibrePoincare.matrixEntryIntrinsicSpectralGradient","GinibrePoincare.matrixEntryRealIndexEquiv","GinibrePoincare.matrixFullSymmetricSpectralLift","GinibrePoincare.matrixFullSymmetricSpectralLift_differentiableAt","GinibrePoincare.matrixFullSymmetricSpectralLift_eventually_eq_simple","GinibrePoincare.matrixRealCoordinates","GinibrePoincare.matrixSymmetricLift","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","Matrix","Matrix.charpoly","Matrix.of","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.single","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","Polynomial.Separable","PolynormableSpace.continuousSMul","Prod","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instOne","Real.instRCLike","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Sigma","Sigma.instDecidableEqSigma","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","WithLp.ofLp","congrArg","fderiv","id","instCommCStarAlgebraComplex","instContinuousSMulForall","instDecidableEqFin","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralLiftFullEntry","name":"GinibrePoincare.matrixEntryFullSpectralLift_derivative_locallyIntegrable","type_dependencies":["AddCommGroup.toAddCommMonoid","CommCStarAlgebra.toNormedCommRing","C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ormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithLp.ofLp","fact_one_le_two_ennreal","fderiv","instCommCStarAlgebraComplex","instFintypeProd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.matrixEntryGaussianDensityReal","type_dependencies":["Equiv","Fin","GinibrePoincare.Configuration","Nat","Prod","Real"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixGaussianDensityReal","InnerProductSpace.toNormedSpace","Matrix","Matrix.of","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.matrixEntryGaussianDensityReal_continuous","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous","Equiv","Fin","GinibrePoincare.Configuration","GinibrePoincare.matrixEntryGaussianDensityReal","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","Complex","Complex.continuous_normSq","Complex.instAddCommMonoid","Complex.instSemiring","Complex.normSq","Continuous","Continuous.comp'","Continuous.const_mul","Continuous.matrixOf","Continuous.rexp","ContinuousLinearEquiv","ContinuousLinearEquiv.continuousSemilinearEquivClass","ContinuousLinearEquiv.equivLike","ContinuousMapClass.map_continuous","ContinuousSemilinearEquivClass.continuousSemilinearMapClass","ContinuousSemilinearMapClass.toContinuousMapClass","DFunLike.coe","DivInvMonoid.toDiv","Eq","Eq.mpr","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixEntryGaussianDensityReal","GinibrePoincare.matrixGaussianDensityReal","GinibrePoincare.matrixHSNormSq","GinibrePoincare.matrixHSNormSq_eq_sum","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Matrix","Matrix.of","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedField","Real.pi","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","congrArg","continuous_apply","continuous_finsetSum","funext","id","instCommCStarAlgebraComplex","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulNat","instMulZeroOneClassOfSemiring","instTopologicalSpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.matrixEntryGaussianDensityReal_pos","type_dependencies":["Equiv","Fin","GinibrePoincare.Configuration","GinibrePoincare.matrixEntryGaussianDensityReal","LT.lt","Nat","OfNat.ofNat","Prod","Real","Real.instLT","Real.instZero","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixGaussianDensityReal_pos","InnerProductSpace.toNormedSpace","LT.lt","Matrix","Matrix.of","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.matrixEntryGaussianMeasure","type_dependencies":["Complex","Complex.measurableSpace","Equiv","Fin","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.Measure","Nat","Prod"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixGaussianDensity","InnerProductSpace.toNormedSpace","Matrix","Matrix.of","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.matrixEntryGaussianMeasure.eq_1","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixComplexEntryEquiv","GinibrePoincare.matrixEntryGaussianMeasure","GinibrePoincare.matrixGaussianDensity","InnerProductSpace.toNormedSpace","Matrix","Matrix.of","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.measurableSpace","Eq.refl","Equiv","Fin","GinibrePoincare.Configuration","GinibrePoincare.matrixEntryGaussianMeasure","MeasurableSpace.pi","MeasureTheory.Measure","Nat","Prod"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevProductGaussian","name":"GinibrePoincare.matrixEntryGaussianMeasure_eq_product","type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OfNatNat","instSMulOfMul","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurDensity","name":"GinibrePoincare.matrixHSNormSq_unitary_conjugation","type_dependencies":["AddCommMonoid.toAddMonoid","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Eq","Fin","Fin.fintype","GinibrePoincare.matrixHSNormSq","HMul.hMul","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","Real","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","instDecidableEqFin","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","CommMagma.toMul","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.re","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","GinibrePoincare.matrixHSNormSq","HMul.hMul","Iff.mp","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.conjTranspose_conjTranspose","Matrix.conjTranspose_mul","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instStar","Matrix.mem_unitaryGroup_iff'","Matrix.mul_assoc","Matrix.nonUnitalSemiring","Matrix.one","Matrix.one_mul","Matrix.semiring","Matrix.trace","Matrix.trace_mul_comm","Matrix.unitaryGroup","Membership.mem","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSemiring.toNonUnitalNonAssocSemiring","NonUnitalSemiring.toSemigroupWithZero","OfNat.ofNat","One.toOfNat1","Real","Ring.toAddGroupWithOne","Semigroup.toMul","SemigroupWithZero.toSemigroup","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","Trans.trans","True","congr","congrArg","congrFun'","eq_self","id","instDecidableEqFin","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instTransEq","mul_assoc","mul_one","of_eq_true"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"GinibrePoincare.matrixInverseCayley","type_dependencies":["Complex","Fin","Matrix","Nat"],"value_dependencies":["Complex","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instOne","Complex.instSub","Complex.instZero","Fin","Fin.fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Inv.inv","Matrix","Matrix.add","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.inv","Matrix.one","Matrix.sub","Nat","OfNat.ofNat","One.toOfNat1","instDecidableEqFin","instHAdd","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"GinibrePoincare.matrixInverseCayley.eq_1","type_dependencies":["Complex","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instOne","Complex.instSub","Complex.instZero","Eq","Fin","Fin.fintype","GinibrePoincare.matrixInverseCayley","HAdd.hAdd","HMul.hMul","HSub.hSub","Inv.inv","Matrix","Matrix.add","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.inv","Matrix.one","Matrix.sub","Nat","OfNat.ofNat","One.toOfNat1","instDecidableEqFin","instHAdd","instHSub"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.matrixInverseCayley","Matrix","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"GinibrePoincare.matrixInverseCayley_cayley","type_dependencies":["Complex","Complex.instOne","Complex.instSemiring","Complex.instSub","Complex.instZero","Eq","Fin","Fin.fintype","GinibrePoincare.matrixCayley","GinibrePoincare.matrixInverseCayley","HSub.hSub","IsUnit","Matrix","Matrix.one","Matrix.semiring","Matrix.sub","Nat","OfNat.o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","module":"GinibrePoincare.Analysis.MatrixUnitaryLowerChart","name":"GinibrePoincare.matrixLowerRead._proof_2","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.addCommGroup","Complex.instNormedField","ContinuousAdd","GinibrePoincare.SchurLowerIndex","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instNormedField","GinibrePoincare.SchurLowerIndex","IsTopologicalAddGroup.toContinuousAdd","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.addCommGroup","Pi.isTopologicalAddGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixUnitaryLowerChart","name":"GinibrePoincare.matrixLowerRead._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Field.toCommRing","Field.toSemifield","GinibrePoincare.SchurLowerIndex","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SMulCommClass","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Field.toCommRing","Field.toSemifield","GinibrePoincare.SchurLowerIndex","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixUnitaryLowerChart","name":"GinibrePoincare.matrixLowerRead._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousConstSMul","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.SchurLowerIndex","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Comple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o","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormMulClass.toNoZeroDivisors","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.exp","NormedSpace.exp.congr_simp","NormedSpace.exp_zero","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OpenPartialHomeomorph.open_source","OpenPartialHomeomorph.toPartialHomeomorph","PartialEquiv.source","PartialHomeomorph.toPartialEquiv","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instZero","Pi.topologicalSpace","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SProd.sprod","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.InjOn","Set.InjOn.mono","Set.instInter","Set.instMembership","Set.instSProd","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Submonoid","Submonoid.instSetLike","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.MatrixSchurAngularChart.0.GinibrePoincare.matrixSchurAngularChart_exists._simp_1_1","congrArg","congrFun'","continuous_const","continuous_id","eq_self","id","instCommCStarAlgebraComplex","instContinuousAddMatrix","instContinuousSMulForall","instContinuousSMulMatrix","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instSeparatelyContinuousAddOfContinuousAdd","instTopologicalSpaceMatrix","instTopologicalSpaceProd","instTopologicalSpaceSubtype","isOpen_ne_fun","isReduced_of_noZeroDivisors","isUnit_iff_ne_zero","map_zero","mul_one","of_eq_true","pow_ne_zero","two_smul"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSchurExponentialJacobian","name":"GinibrePoincare.matrixSchurAngularDensity","type_dependencies":["Complex","GinibrePoincare.SchurLowerIndex","Nat","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap.comp","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Fin","GinibrePoincare.SchurLowerIndex","GinibrePoincare.matrixLowerRead","GinibrePoincare.matrixSchurAngularDensity._proof_1","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixUnitaryConnection","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.det","Matrix","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.module","Module.End.instSemiring","MonoidHom","MonoidHom.instFunLike","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddGroup","Real.instRCLike","Real.lattice","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","abs","fderiv","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instTopologicalSpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurExponentialJacobian","name":"GinibrePoincare.matrixSchurAngularDensity._proof_1","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis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hurAtlasChart.eq_1","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Complex.instZero","Eq","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurFrameChart","HMul.hMul","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.zero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","OfNat.ofNat","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Zero.toOfNat0"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.matrixSchurAtlasChart","Matrix","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurGlobalIntegration","name":"GinibrePoincare.matrixSchurAtlasChart_continuous","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Continuous","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAtlasChart","Matrix","Nat","NormedCommRing.toSeminormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instTopologicalSpaceMatrix","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.instZero","Continuous","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.continuous","DistribMulAction.toMulAction","Eq","Eq.mpr","Eq.symm","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Function.comp","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialChart_differentiable","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurFrameChart","GinibrePoincare.matrixUnitaryConjugation","GinibrePoincare.matrixUnitaryConjugation_apply","GinibrePoincare.schurUpperCombination","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","List.finRange","List.foldr","List.map","Matrix","Matrix.add","Matrix.addCommGroup","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.module","Matrix.of","Matrix.zero","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.topologicalSpace","PolynormableSpace.continuousSMul","Prod.continuousAdd","Prod.continuousSMul","Prod.fst","Prod.instAddCommGroup","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","instCommCStarAlgebraComplex","instContinuousAddMatrix","instContinuousSMulForall","instContinuousSMulMatrix","instHAdd","instHMul","instInnerProductSpaceRealComplex","instPolynormableSpace","instTopologicalSpaceMatrix","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurAtlasOverlap","name":"GinibrePoincare.matrixSchurAtlasChart_eq_conjugation","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Eq","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.schurUpperCombination","HMul.hMul","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","Prod.fst","Prod.snd","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Complex.instZero","Distrib.toMul","Eq","Eq.mpr","Eq.trans","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurFrameChart","GinibrePoincare.schurUpperCombination","HAdd.hAdd","HMul.hMul","InvolutiveStar.toStar","Matrix","Matrix.add","Matrix.addZeroClass","Matrix.conjTranspose","Matrix.conjTranspose_mul","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.nonUnitalSemiring","Matrix.zero","Nat","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSemiring.toSemigroupWithZero","OfNat.ofNat","Prod.fst","Prod.snd","Semigroup.toMul","SemigroupWithZero.toSemigroup","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","True","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","id","instHAdd","instHMul","mul_assoc","of_eq_true","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurGlobalIntegration","name":"GinibrePoincare.matrixSchurAtlasChart_injOn","type_dependencies":["CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instStarRing","Complex.instZero","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurFrameChart","Matrix","Matrix.semiring","Matrix.unitaryGroup","Matrix.zero","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","OfNat.ofNat","Set","Set.InjOn","SetLike.instMembership","Submonoid","Submonoid.instSetLike","Subtype","Subtype.val","Zero.toOfNat0","instDecidableEqFin","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddCommMonoid.toAddMonoid","CommCStarAlgebra.toNormedCommRing","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Eq.mpr","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurFrameChart","GinibrePoincare.matrixUnitaryConjugation","GinibrePoincare.matrixUnitaryConjugation_apply","GinibrePoincare.matrixUnitaryConjugation_injective","HMul.hMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.of","Matrix.semiring","Matrix.unitaryGroup","Matrix.zero","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSp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at","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toNonUnitalNonAssocSemiring","NonUnitalSemiring.toSemigroupWithZero","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Polynomial.Separable","Preorder.toLT","Prod","Prod.Lex.instLT","Prod.Lex.instPreorder","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","Real","Real.instLT","Real.instPreorder","Real.instRCLike","Real.normedField","Real.semiring","Ring.toAddGroupWithOne","RingHom.id","SProd.sprod","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.instSProd","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","Subtype","Subtype.mk","Subtype.property","Subtype.val","Trans.trans","True","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","instLTFin","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instTransEq","mul_assoc","of_eq_true","toLex","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurAtlasOverlap","name":"GinibrePoincare.matrixSchurAtlas_flag_overlap","type_dependencies":["AddCommMonoid.toAddMonoid","And","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instStarRing","Eq","Exists","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurSortedUpperDomain","GinibrePoincare.matrixUnitaryFlagSaturation","HMul.hMul","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","Subtype","Subtype.val","instDecidableEqFin","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","And","And.casesOn","And.intro","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.im","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.re","DFunLike.coe","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Fin.instPartialOrder","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixDiagonalUnitary_schur_preserves","GinibrePoincare.matrixSchurAtlasChart","GinibrePoincare.matrixSchurAtlasChart_eq_conjugation","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurOrderedDiagonal","GinibrePoincare.matrixSchurSortedUpperDomain","GinibrePoincare.matrixUnitaryFlagSaturation","GinibrePoincare.schurEntryCoordinates","GinibrePoincare.schurUpperCombination","GinibrePoincare.schurUpperCombination_lower_zero","GinibrePoincare.schurUpperCombination_read_upper","HMul.hMul","Iff.mp","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","LT.lt","Lex","LinearMap","LinearMap.instFunLike","Matrix","Matrix.addCommMonoid","Matrix.conjTranspose","Matrix.conjTranspose_mul","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instStar","Matrix.mem_unitaryGroup_iff","Matrix.module","Matrix.mul_assoc","Matrix.nonUnitalSemiring","Matrix.one","Matrix.one_mul","M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roup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","ContinuousAdd.measurableAdd","ContinuousLinearMap.det","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivisionRing.toRing","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","Eq.mp","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toDivisionRing","Fin","Fin.decLe","Fin.decLt","Fin.fintype","Finite.instProd","Finite.of_fintype","Finite.to_countable","FiniteDimensional.finiteDimensional_pi'","Function.Injective","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurAngularDensity","GinibrePoincare.matrixSchurEntryChart","GinibrePoincare.matrixSchurEntryChart_hasFDerivAt","GinibrePoincare.matrixSchurEntryChart_injOn","GinibrePoincare.matrixSchurEntryDerivative","GinibrePoincare.matrixSchurEntryDerivative_abs_det","GinibrePoincare.schurLocalChart","GinibrePoincare.schurUpperCombination","GinibrePoincare.vandermondeWeight","HAdd.hAdd","HMul.hMul","HasFDerivAt.hasFDerivWithinAt","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Lex","Lex.fintype","Matrix","Matrix.add","MeasurableSet","MeasurableSpace.pi","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.instIsAddHaarMeasureForallVolumeOfMeasurableAddOfSigmaFinite","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.Measure.prod.instIsAddHaarMeasure","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.lintegral","MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul","Membership.mem","MetricSpace.toEMetricSpace","Module.Finite.prod","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","OpenPartialHomeomorph.toPartialHomeomorph","OrderDual","OrderDual.fintype","OrderDual.ofDual","PartialEquiv.source","PartialHomeomorph.toPartialEquiv","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.addGroup","Pi.borelSpace","Pi.measurableAdd","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","Prod.borelSpace","Prod.fst","Prod.instAddCommGroup","Prod.instMeasurableSpace","Prod.instModule","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddGroup","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.lattice","Real.normedField","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.InjOn.mono","Set.image","Set.instLE","Set.instMembership","SubNegMonoid.toAddMonoid","Subtype.countable","Subtype.finite","Subtype.fintype","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","congrArg","congrFun'","funext","instCommCStarAlgebraComplex","instCountableFin","instCountableProd","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instInnerProductSpac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ero_add"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSchurFrameJacobian","name":"GinibrePoincare.matrixSchurFrameNormalizedDerivative","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAddCommMonoid","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","InnerProductSpace.toNormedSpace","LinearMap","Matrix","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Prod.instAddCommMonoid","Prod.instModule","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","ContinuousLinearMap.comp","ContinuousLinearMap.toLinearMap","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurFrameChart","GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_1","GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_2","GinibrePoincare.matrixUnitaryConjugation","GinibrePoincare.schurEntryCoordinates","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","LinearMap.comp","Matrix","Matrix.addCommMonoid","Matrix.conjTranspose","Matrix.module","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instTopologicalSpaceProd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurFrameJacobian","name":"GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_1","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurFrameJacobian","name":"GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_2","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurFrameJacobian","name":"GinibrePoincare.matrixSchurFrameNormalizedDerivative.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","ContinuousLinearMap.comp","ContinuousLinearMap.toLinearMap","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.matrixSchurFrameChart","GinibrePoincare.matrixSchurFrameNormalizedDerivative","GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_1","GinibrePoincare.matrixSchurFrameNormalizedDerivative._proof_2","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Monoid","Real.instCommSemiring","Real.instDivisionRing","Real.instInv","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toMonoid","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","contDiff_const_smul","instContinuousConstSMulForall","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instTopENat","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpatialCutoff","name":"GinibrePoincare.matrixSpatialCutoff_tendsto","type_dependencies":["Filter.Tendsto","Filter.atTop","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instOne","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","nhds"],"value_dependencies":["Algebra.toSMul","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instZero","ContDiffBump","ContDiffBump.continuous","ContDiffBump.one_of_mem_closedBall","ContDiffBump.toFun","ContDiffBump.toFun.congr_simp","Continuous.continuousAt","ContinuousAt.tendsto","Dist.dist","DistribLattice.toLattice","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mp","Eq.refl","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.smul_const","Filter.atTop","Filter.tendsto_atTop_add_const_right","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","Function.comp","Function.hasSMul","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialBump","GinibrePoincare.matrixSpatialCutoff","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","LE.le","Lattice.toSemilatticeInf","Membership.mem","Metric.closedBall","Metric.mem_closedBall._simp_1","Module.toMulActionWithZero","MulActionWithZero.toSMulWithZero","MulZeroClass.toZero","Nat","Nat.cast","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.addCommGroup","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.smulWithZero","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instAdd","Real.instAddCommGroup","Real.instArchimedean","Real.instDivisionRing","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoidWithZero","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Set","Set.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","dist_self","id","instContinuousSMulForall","instDistribLatticeOfLinearOrder","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOrderTopologyReal","instPolynormableSpace","nhds","of_eq_true","pseudoMetricSpacePi","tendsto_inv_atTop_zero","tendsto_natCast_atTop_atTop","zero_le_one._simp_1","zero_smul"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixGaussianH1LSI","name":"GinibrePoincare.matrixSpatialTruncation","type_dependencies":["GinibrePoincare.MatrixRealSpace","Nat","Real"],"value_dependencies":["GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","HMul.hMul","Nat","Real","Real.instMul","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianH1LSI","name":"GinibrePoincare.matrixSpatialTruncation.eq_1","type_dependencies":["Eq","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","GinibrePoincare.matrixSpatialTruncation","HMul.hMul","Nat","Real","Real.instMul","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialTruncation","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianH1LSI","name":"GinibrePoincare.matrixSpatialTruncation_L2_errors","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Field.toSemifield","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialTruncation","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMonoid","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","fderiv","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.left","And.right","Bool","Bool.false","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","Continuous.aestronglyMeasurable","Continuous.clm_apply","Continuous.pow","Continuous.sub","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.pow","Filter.Tendsto.sub_const","Filter.atTop","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","GinibrePoincare.matrixSpatialCutoff_derivative_bound","GinibrePoincare.matrixSpatialCutoff_mem_unit","GinibrePoincare.matrixSpatialTruncation","GinibrePoincare.matrixSpatialTruncation_contDiff","GinibrePoincare.matrixSpatialTruncation_fderiv","GinibrePoincare.matrixSpatialTruncation_limits","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProduc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ormedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.mul","ContDiff.of_le","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Eq.trans","False","Fin","Fin.fintype","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","GinibrePoincare.matrixSpatialCutoff_smooth","InnerProductSpace.toNormedSpace","LE.le","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Preorder.toLE","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","True","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","congrArg","instInnerProductSpaceRealComplex","instOneENat","instOrderTopENat","instPreorderENat","instTopENat","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianH1LSI","name":"GinibrePoincare.matrixSpatialTruncation_direction_energy_tendsto","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Field.toSemifield","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialTruncation","HPow.hPow","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And","And.casesOn","And.right","Bool","Bool.false","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff","ContDiff.continuous_fderiv","Continuous.aestronglyMeasurable","Continuous.clm_apply","Continuous.pow","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toSemifield","Filter.Tendsto","Filter.Tendsto.pow","Filter.atTop","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.MatrixRealSpace","GinibrePoincare.matrixSpatialCutoff","GinibrePoincare.matrixSpatialCutoff_derivative_bound","GinibrePoincare.matrixSpatialCutoff_mem_unit","GinibrePoincare.matrixSpatialTruncation","GinibrePoincare.matrixSpatialTruncation_contDiff","GinibrePoincare.matrixSpatialTruncation_fderiv","GinibrePoincare.matrixSpatialTruncation_limits","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toMulPosStrictMono","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.natCast_nonneg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.Integrable.add","MeasureTheory.Integrable.const_mul","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable_sq","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.tendsto_integral_of_dominated_convergence","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSuc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","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","abs","abs_of_nonneg","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","fderiv","id","inferInstance","instCountableFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSecondCountableTopologyReal","le_of_not_gt","mul_le_mul_of_nonneg_right","mul_nonneg_of_nonpos_of_nonpos","nhds","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralLiftLSITransport","name":"GinibrePoincare.matrixSpectralLift_H1_energy","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearEquiv","ContinuousLinearEquiv.equivLike","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Filter.EventuallyEq","Fin","Function.comp","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.MatrixGaussianL2","GinibrePoincare.MatrixGaussianL2._proof_1","GinibrePoincare.MatrixGaussianSobolevPair","GinibrePoincare.MatrixGaussianSobolevPair._proof_1","GinibrePoincare.MatrixRealIndex","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.matrixGaussianMeasure","GinibrePoincare.matrixGaussianSobolevEnergy","GinibrePoincare.matrixRealCoordinates","GinibrePoincare.matrixSpectralOverlapEnergy","GinibrePoincare.matrixSymmetricLift","HMul.hMul","InnerProductSpace.toNormedSpace","Matrix","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.single","Pi.topologicalSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Sigma","Sigma.instDecidableEqSigma","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fderiv","instCommCStarAlgebraComplex","instDecidableEqFin","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_d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ormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Fintype.card","Fintype.card_fin","Fintype.card_prod","Fintype.equivOfCardEq","Function.comp","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.ginibreMeasure","GinibrePoincare.matrixGaussianMeasure","GinibrePoincare.matrixSpectralLift_finite_overlap_gaussian_poincare_of_entries","GinibrePoincare.matrixSpectralOverlapEnergy","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.mul_pos","Nat.sub_add_cancel","Nat.succ_le_of_lt","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","congr","congrArg","id","instAddNat","instCommCStarAlgebraComplex","instFintypeProd","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instLENat","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeMatrixPoincare","name":"GinibrePoincare.matrixSpectralLift_finite_overlap_gaussian_poincare_of_entries","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Function.comp","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.ginibreMeasure","GinibrePoincare.matrixGaussianMeasure","GinibrePoincare.matrixSpectralOverlapEnergy","GinibrePoincare.smoothGinibreVariance","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Matrix","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.MemLp","MeasureTheory.integral","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instAddNat","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommCStarAlgebra.toNormedCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex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brePoincare.Analysis.MatrixSymmetricLift","name":"GinibrePoincare.matrixSpectralOverlapEnergy","type_dependencies":["Complex","Fin","GinibrePoincare.GinibreMatrixCoordinates","Nat","Real"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Fin","Fin.fintype","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixEigenvalueProjector","GinibrePoincare.matrixMeasurableEigenvalues","GinibrePoincare.matrixOverlapEnergy","GinibrePoincare.realDifferentialWirtinger","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixOverlapLowerBound","name":"GinibrePoincare.matrixSpectralOverlapEnergy_ge_gradient","type_dependencies":["Complex","Complex.commRing","Complex.instCommSemiring","DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixMeasurableEigenvalues","GinibrePoincare.matrixSpectralOverlapEnergy","GinibrePoincare.realGradientNormSq","HMul.hMul","LE.le","Matrix","Matrix.charpoly","Matrix.of","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Polynomial.Separable","Real","Real.instLE","Real.instMul","Real.instNatCast","instDecidableEqFin","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instNormedField","Complex.instSemiring","Complex.normSq","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Eq.mpr","Eq.refl","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.GinibreMatrixCoordinates","GinibrePoincare.matrixEigenvalueProjector_overlap_ge","GinibrePoincare.matrixMeasurableEigenvalues","GinibrePoincare.matrixSpectralOverlapEnergy","GinibrePoincare.realDifferentialWirtinger","GinibrePoincare.realGradientNormSq","GinibrePoincare.realGradientNormSq_eq_wirtinger","HMul.hMul","InnerProductSpace.toNormedSpace","IsOrderedRing.toPosMulMono","LE.le","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Matrix","Matrix.charpoly","Matrix.of","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","Polynomial.Separable","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fderiv","id","instDecidableEqFin","instHMul","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_le_mul_of_nonneg_left"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixGinibreSymmetrizedLaw","name":"GinibrePoincare.matrixSpectralPermutationAverage","type_dependencies":["Complex","ENNReal","Fin","Nat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoid","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instInv","Equiv","Equiv.instEquivLike","Equiv.instFintype","EquivLike.toFunLike","Fin","Fin.fintype","Finset.sum","Finset.univ","Fintype.card","Function.comp","HMul.hMul","Inv.inv","Nat","Nat.cast","instDecidableEqFin","instDistribOfSemiring","instH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ormedAddCommGroup","Pi.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedField","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submonoid","Submonoid.instSetLike","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_inv","abs_zero","congrArg","congrFun'","eq_false","instCommCStarAlgebraComplex","instCountableFin","instDecidableEqFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHSMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroOneClassOfSemiring","instSMulOfMul","instSeparatelyContinuousAddOfContinuousAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","inv_one","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","one_smul","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSchurFrameDerivative","name":"GinibrePoincare.matrixUnitaryConnection","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Fin","GinibrePoincare.SchurLowerIndex","InnerProductSpace.toNormedSpace","Matrix","Matrix.addCommMonoid","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instTopologicalSpaceMatrix"],"value_dependencies":["AddCommMonoid.toAddMonoid","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.mul","ContinuousLinearMap.restrictScalars","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.SchurLowerIndex","GinibrePoincare.matrixUnitaryConnection._proof_1","GinibrePoincare.matrixUnitaryConnection._proof_2","GinibrePoincare.matrixUnitaryConnection._proof_3","GinibrePoincare.matrixUnitaryConnection._proof_4","GinibrePoincare.matrixUnitaryConnection._proof_5","GinibrePoincare.matrixUnitaryConnection._proof_6","GinibrePoincare.matrixUnitaryConnection._proof_7","GinibrePoincare.matrixUnitaryConnection._proof_8","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","Matrix","Matrix.addCommMonoid","Matrix.conjTranspose","Matrix.linftyOpNonUnitalSemiNormedRing","Matrix.linftyOpNormedSpace","Matrix.module","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCom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ormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_1","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_10","type_dependencies":["Algebra.id","Algebra.toSMul","Complex","Complex.instCommSemiring","Complex.instSemiring","Distrib.toMul","Fin","Fin.fintype","Matrix","Matrix.instAlgebra","Matrix.semiring","Nat","SMulCommClass","instDecidableEqFin","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.id","Algebra.to_smulCommClass","Complex","Complex.instCommSemiring","Complex.instSemiring","Fin","Fin.fintype","Matrix","Matrix.instAlgebra","Matrix.semiring","Nat","instDecidableEqFin"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_11","type_dependencies":["AddCommGroup.toAddGroup","CommCStarAlgebra.toNormedCommRing","Complex","Fin","Fin.fintype","IsTopologicalAddGroup","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Fin","Fin.fintype","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_12","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","ContinuousAdd","Distrib.toAdd","Fin","Fin.fintype","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Nat","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Fin","Fin.fintype","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Nat","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_13","type_dependencies":["AddCommMonoid.toAddMonoid","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.instDenselyNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Field.toCommRing","Field.toSemifield","Fin","Fin.fintype","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Matrix.linftyOpNormedSpace","Module.toDis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rePoincare.matrixUnitaryRealMap._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instDenselyNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","Fin","Fin.fintype","InnerProductSpace.toNormedSpace","LinearMap.CompatibleSMul","Matrix","Matrix.linftyOpNonUnitalSemiNormedRing","Matrix.linftyOpNormedSpace","Matrix.linftyOpSeminormedAddCommGroup","Matrix.module","Module.toDistribMulAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Real","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instRCLike","Complex.instSemiring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","Fin","Fin.fintype","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.right","LinearMap.IsScalarTower.compatibleSMul","Matrix","Matrix.addCommGroup","Matrix.isScalarTower","Matrix.linftyOpNonUnitalSemiNormedRing","Matrix.linftyOpNormedSpace","Matrix.linftyOpSeminormedAddCommGroup","Matrix.module","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_3","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instDenselyNormedField","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.instDenselyNormedField","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","name":"GinibrePoincare.matrixUnitaryRealMap._proof_4","type_dependencies":["AddCommGroup.toAddGroup","CommCStarAlgebra.toNormedCommRing","Complex","Fin","Fin.fintype","IsTopologicalAddGroup","Matrix","Matrix.linftyOpSeminormedAddCommGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSe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oid.toAddMonoid","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","ContinuousLinearEquiv","ContinuousLinearEquiv.apply_symm_apply","ContinuousLinearEquiv.equivLike","ContinuousLinearEquiv.symm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Eq.mpr","Eq.symm","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.MatrixRealIndex","GinibrePoincare.matrixHSNormSq","GinibrePoincare.matrixHSNormSq_unitary_conjugation","GinibrePoincare.matrixRealCoordinates","GinibrePoincare.matrixRealCoordinates_HS","GinibrePoincare.matrixUnitaryRealMap","GinibrePoincare.matrixUnitaryRealMap_apply","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","Matrix","Matrix.conjTranspose","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.of","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","Monoid.toNPow","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Sigma","Sigma.instFintype","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submonoid","Submonoid.instSetLike","UniformSpace.toTopologicalSpace","congrArg","id","instDecidableEqFin","instHPow","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixUnitaryCenteredPhaseFactorization","name":"GinibrePoincare.matrixUnitary_centered_phase_factorization","type_dependencies":["And","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAdd","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Eq","Exists","Filter","Filter.Eventually","Filter.instMembership","Fin","Fin.fintype","GinibrePoincare.MatrixSkewCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.matrixUnitaryPhaseLocalChart","GinibrePoincare.matrixUnitaryPhaseParameter","HAdd.hAdd","IsUnit","Matrix","Matrix.add","Matrix.one","Matrix.semiring","Matrix.unitaryGroup","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","OpenPartialHomeomorph.toPartialHomeomorph","PartialEquiv.source","PartialHomeomorph.toPartialEquiv","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Set","Set.instMembership","SetLike.instMembership","Submonoid","Submonoid.instSetLike","UniformSpace.toTopologicalSpace","instDecidableEqFin","instHAdd","instMulZeroOneClassOfSemiring","instTopologicalSpaceMatrix","instTopologicalSpaceProd","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instStarRing","Complex.instT2Space","Complex.instZero","Continuous.continuousAt","Continuous.matrix_det","ContinuousAt","ContinuousAt.add_const","ContinuousAt.comp","ContinuousAt.comp'","ContinuousAt.eventually_ne","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousSMul.continuousConstSMul","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Eq","Eq.mpr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ousInv\u2080","Measurable.sub","MeasurableInv.measurable_inv","MetricSpace.toEMetricSpace","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instAddGroup","Real.instDivisionRing","Real.instField","Real.instInv","Real.instOne","Real.instSub","Real.measurableSpace","Real.metricSpace","Real.pseudoMetricSpace","Semifield.toDivisionSemiring","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupReal","instIsTopologicalDivisionRingReal","instSecondCountableTopologyReal","instT6SpaceOfMetrizableSpace","measurable_const"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeL2Inverse","name":"GinibrePoincare.measurable_inverseVandermondeMultiplier","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.inverseVandermondeMultiplier","Measurable","MeasurableSpace.pi","Nat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Complex.ofReal","Continuous.measurable","ContinuousInv\u2080.measurableInv","ContinuousMul.measurableMul\u2082","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.continuous_vandermonde","GinibrePoincare.groundStateNormalization","GinibrePoincare.inverseVandermondeMultiplier","GinibrePoincare.vandermonde","Inv.inv","IsTopologicalDivisionRing.toContinuousInv\u2080","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Measurable","Measurable.inv","Measurable.mul","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Semifield.toDivisionSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","id","instCountableFin","instT6SpaceOfMetrizableSpace","measurable_const","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixGaussianMeasure","name":"GinibrePoincare.measurable_matrixGaussianDensity","type_dependencies":["Complex","ENNReal","ENNReal.measurableSpace","Fin","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.matrixGaussianDensity","Matrix","Measurable","Nat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous.measurable","ContinuousAdd.measurableMul\u2082","ContinuousMul.measurableMul","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.measurableSpace","ENNReal.ofReal","Eq","Eq.mpr","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.measurable_sum","Finset.sum","Finset.univ","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.matrixGaussianDensity","GinibrePoincare.matrixHSNormSq","GinibrePoincare.matrixHSNormSq_eq_sum","HDiv.hDiv","HMul.hMul","HPow.hPow","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Matrix","Measurable","Measurable.const_mul","Measurable.ennreal_ofReal","Measurable.exp","Measurable.fun_comp","MeasurableSpace.pi","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.measurableSpace","Real.pi","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","congrArg","funext","id","instHDiv","instHMul","instHPow","instIsTopologicalRingReal","instMulNat","instMulZeroOneClassOfSemiring","instSecondCountableTopologyReal","measurable_pi_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurAngularDensity","name":"GinibrePoincare.measurable_matrixSchurAngularDensity","type_dependencies":["Complex","Complex.measurableSpace","GinibrePoincare.SchurLowerIndex","GinibrePoincare.matrixSchurAngularDensity","Measurable","MeasurableSpace.pi","Nat","Real","Real.measurableSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","BorelSpace.opensMeasurable","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toCommSemiring","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","Continuous.clm_comp","Continuous.fst","Continuous.matrix_conjTranspose","Continuous.measurable","Continuous.snd","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.continuous_det","ContinuousLinearMap.continuous_restrictScalars","ContinuousLinearMap.det","ContinuousLinearMap.funLike","ContinuousLinearMap.instBorelSpace","ContinuousLinearMap.instMeasurableSpace","ContinuousLinearMap.measurable_comp","ContinuousLinearMap.module","ContinuousLinearMap.mul","ContinuousLinearMap.restrictScalars","ContinuousLinearMap.toLinearMap","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable.continuous","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Fin","Fin.decLt","Fin.fintype","Finite.of_fintype","Finite.to_countable","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.proper_real","GinibrePoincare.SchurLowerIndex","GinibrePoincare.ginibreMatrixMeasurableSpace","GinibrePoincare.matrixLowerRead","GinibrePoincare.matrixSchurAngularDensity._proof_1","GinibrePoincare.matrixSchurExponentialFrame","GinibrePoincare.matrixSchurExponentialFrame_differentiable","GinibrePoincare.matrixUnitaryConnection","GinibrePoincare.matrixUnitaryConnection._proof_1","GinibrePoincare.matrixUnitaryConnection._proof_2","GinibrePoincare.matrixUnitaryConnection._proof_3","GinibrePoincare.matrixUnitaryConnection._proof_4","GinibrePoincare.matrixUnitaryConnection._proof_5","GinibrePoincare.matrixUnitaryConnection._proof_6","GinibrePoincare.matrixUnitaryConnection._proof_7","GinibrePoincare.matrixUnitaryConnection._proof_8","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsModuleTopology.toContinuousSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","Lex","Lex.fintype","LinearMap","LinearMap.det","Matrix","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.conjTranspose","Matrix.instCompleteSpace","Matrix.instUniformSpace","Matrix.isScalarTower","Matrix.linftyOpNonUnitalSemiNormedRing","Matrix.linftyOpNormedAddCommGroup","Matrix.linftyOpNormedRing","Matrix.linftyOpNormedSpace","Matrix.linftyOpSemiNormedRing","Matrix.linftyOpSeminormedAddCommGroup","Matrix.module","Measurable","Measurable.comp","Measurable.fun_comp","Measurable.prodMk","MeasurableSpace.pi","MetricSpace.toEMetricSpace","Module.End.instSemiring","Module.Finite.matrix","Module.Free.of_divisionRing","Module.toDistribMulAction","Monoid.toSemigroup","MonoidHom","MonoidHom.instFunLike","MulAction.toSemigroupAction","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalRing.toNonUnitalNonAssocRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toNonUnitalRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toMetricSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OrderDual","OrderDual.fintype","OrderDual.ofDual","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.isTopologicalAddGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","Prod.opensMeasurableSpace","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCompleteSpace","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instRCLike","Real.linearOrder","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","Subtype.countable","Subtype.finite","Subtype.fintype","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.MatrixSchurAngularDensity.0.GinibrePoincare.measurable_matrixSchurAngularDensity._proof_1_1","abs","continuous_abs","continuous_const","continuous_id'","fderiv","id","instCommCStarAlgebraComplex","instContinuousAddMatrix","instContinuousSMulForall","instContinuousSMulMatrix","instDecidableEqFin","instDistribLatticeOfLinearOrder","instFintypeProd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupMatrix","instLTFin","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOrderTopologyReal","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instPolynormableSpace","instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional","instT6SpaceOfMetrizableSpace","instTopologicalSpaceMatrix","instTopologicalSpaceProd","measurable_fderiv","ofLex","secondCountableTopologyEither_of_right","secondCountable_of_proper","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPotential","name":"GinibrePoincare.measurable_potentialDensity","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.measurableSpace","ENNReal.ofReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialWeight","Measurable","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous","Continuous.comp","Continuous.measurable","Continuous.mul","DFunLike.coe","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.continuous_vandermonde","GinibrePoincare.potentialWeight","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeWeight","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologi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asurable.mul","MeasurableSpace.pi","Membership.mem","MetricSpace.toEMetricSpace","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.exp","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","id","instCommCStarAlgebraComplex","instCountableFin","instDistribOfSemiring","instHMul","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instSecondCountableTopologyReal","measurable_pi_apply","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.measurable_vandermondeDensity","type_dependencies":["Complex","Complex.measurableSpace","ENNReal","ENNReal.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.vandermondeDensity","Measurable","MeasurableSpace.pi","Nat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous.comp","Continuous.measurable","DFunLike.coe","ENNReal","ENNReal.measurableSpace","ENNReal.measurable_ofReal","ENNReal.ofReal","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.continuous_vandermonde","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeWeight","Measurable","Measurable.comp","MeasurableSpace.pi","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","id","instCountableFin","instMulZeroOneClassOfSemiring","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","name":"GinibrePoincare.measurePreserving_actual_withDensity","type_dependencies":["ENNReal","ENNReal.measurableSpace","Function.comp","Measurable","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasurePreserving"],"value_dependencies":["Classical.propDecidable","DFunLike.coe","ENNReal","ENNReal.instZero","ENNReal.measurableSpace","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","HEq","HEq.refl","Measurable","Measurable.indicator","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.ext","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.lintegral_comp","MeasureTheory.MeasurePreserving.measurable","MeasureTheory.MeasurePreserving.mk","MeasureTheory.lintegral","MeasureTheory.lintegral_congr","MeasureTheory.lintegral_indicator","MeasureTheory.withDensity_apply","Membership.mem","Not","OfNat.ofNat","Set","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instMembership","Set.mem_preimage._simp_1","Set.preimage","True","Zero.toOfNat0","congr","congrArg","dite","eq_false","eq_of_heq","eq_self","eq_true","id","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.measurePreserving_complexCoordinateGaussian_mul","type_dependencies":["Complex","Complex.instMul","Complex.instNorm","Complex.measurableSpace","Eq","GinibrePoincare.complexCoordinateGaussianProbability","HMul.hMul","LT.lt","MeasureTheory.MeasurePreserving","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","instHMul","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Complex","Complex.borelSpace","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","DFunLike.coe","ENNReal","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","EquivLike.toFunLike","False","False.elim","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.complexCoordinateGaussianDensity","GinibrePoincare.complexCoordinateGaussianDensity_globalPhase","GinibrePoincare.complexCoordinateGaussianMeasure_eq_withDensity","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexMulMeasurableEquiv","GinibrePoincare.measurable_complexCoordinateGaussianDensity","GinibrePoincare.measurePreserving_complex_mul_of_norm_one","HMul.hMul","LT.lt","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableEquiv.measurable","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.withDensity","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.map_withDensity_comp","MeasureTheory.MeasurePreserving.mk","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","Ne","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Real","Real.instFloorRing","Real.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Zero.toOfNat0","congrArg","congrFun'","funext","id","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","measureSpaceOfInnerProductSpace","norm_zero","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GlobalPhaseAction","name":"GinibrePoincare.measurePreserving_complex_mul_of_norm_one","type_dependencies":["Complex","Complex.borelSpace","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","Eq","FiniteDimensional.rclike_to_real","HMul.hMul","MeasureTheory.MeasurePreserving","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","instHMul","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","BorelSpace.opensMeasurable","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSemiring","Complex.measurableEquivPi","Complex.measurableSpace","Complex.normSq","Complex.sq_norm","Complex.volume_preserving_equiv_pi","Continuous.measurable","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toMulAction","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instCommSemiring","ENNReal.instOne","ENNReal.ofReal","ENNReal.ofReal_one","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","Function.smulCommClass","GinibrePoincare.complexMultiplicationMatrix","GinibrePoincare.det_complexMultiplicationMatrix","GinibrePoincare.toLin_complexMultiplicationMatrix","HMul.hMul","HPow.hPow","HSMul.hSMul","Inv.inv","InvOneClass.toOne","IsModuleTopology.toContinuousSMul","IsScalarTower.left","IsScalarTower.right","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LinearEquiv","LinearMap","LinearMap.addCommMonoid","LinearMap.continuous_of_finiteDimensional","LinearMap.instFunLike","LinearMap.module","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.one_natPow","Matrix","Matrix.addCommMonoid","Matrix.det","Matrix.module","Matrix.toLin'","MeasurableEquiv","MeasurableEquiv.apply_symm_apply","MeasurableEquiv.injective","MeasurableEquiv.instEquivLike","MeasurableEquiv.symm","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.map","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.comp","MeasureTheory.MeasurePreserving.mk","MeasureTheory.MeasurePreserving.symm","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toNPow","Monoid.toSemig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ubtype.opensMeasurableSpace","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreRelativePhaseInvariance.0.GinibrePoincare.measurePreserving_recenteredQuarterTurn._simp_1_3","congrArg","congrFun'","continuous_const","continuous_id","eq_self","funext","id","inferInstance","instContinuousSMulForall","instCountableFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","of_eq_true","rfl","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianStoppingExitLimit","name":"GinibrePoincare.measure_iInter_eq_zero_of_reciprocal_bound","type_dependencies":["DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instZero","Eq","HAdd.hAdd","HDiv.hDiv","LE.le","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.real","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instNatCast","Real.instOne","Set","Set.iInter","Zero.toOfNat0","instHAdd","instHDiv"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Algebra.toModule","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toAdd","DistribMulAction.toMulAction","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toNNRatAlgebra","DivisionSemiring.toSemiring","ENNReal","ENNReal.instZero","Eq","Eq.mp","Field.toSemifield","Filter","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.mul","Filter.atTop","Filter.atTop_neBot","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HasSolidNorm.orderClosedTopology","Iff.mp","IsScalarTower.nnrat","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","MeasurableSpace","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.real","MeasureTheory.measureReal_eq_zero_iff","MeasureTheory.measureReal_mono","MeasureTheory.measureReal_nonneg","MeasureTheory.measure_ne_top","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","Nat","Nat.cast","Nat.instCommSemiring","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.iInter","Set.iInter_subset","StarOrderedRing.toIsOrderedRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","funext","ge_of_tendsto","instArchimedeanNat","instClosedIciTopology","instCommSemiringNNRat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHasSolidNormReal","instInhabitedNat","instIsDirectedOrder","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instNonemptyOfInhabited","le_antisymm","mul_one_div","nhds","normedAlgebraRat","tendsto_const_nhds","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightLocal","name":"GinibrePoincare.measure_restrict_le_weight_multiple","type_dependencies":["Algebra.id","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.ofReal","HSMul.hSMul","Inv.inv","IsScalarTower.right","LE.le","LT.lt","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instPartialOrder","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","Membership.mem","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instLT","Real.instZero","Set","Set.instMembership","Zero.toOfNat0","instDistribOfSemiring","instHSMul","instSMulOfMul"],"value_dependencies":["Algebra.id","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instIsOrderedMonoid","ENNReal.instLE","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.inv_mul_cancel","ENNReal.ofReal","ENNReal.ofReal_le_ofReal","ENNReal.ofReal_ne_top","ENNReal.ofReal_pos","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Filter.mp_mem","Filter.univ_mem'","HMul.hMul","HSMul.hSMul","Iff.mpr","Inv.inv","IsScalarTower.left","IsScalarTower.right","LE.le","LE.le.trans","LT.lt","LT.lt.ne'","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instCovariantClassHSMulLeOfENNReal","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instPartialOrder","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_le_self","MeasureTheory.Measure.withDensity","MeasureTheory.ae","MeasureTheory.ae_restrict_mem","MeasureTheory.restrict_withDensity","MeasureTheory.withDensity_const","MeasureTheory.withDensity_mono","Membership.mem","Monoid.toMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","Ne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.instLE","Real.instLT","Real.instZero","SemigroupAction.toSMul","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","Zero.toOfNat0","congrArg","congrFun'","id","instCovariantClassHSMulLeOfIsOrderedSMul","instDistribOfSemiring","instHMul","instHSMul","instIsOrderedSMulOfIsOrderedMonoid","instSMulOfMul","one_smul","smul_le_smul_left","smul_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LebesgueL2Convolution","name":"GinibrePoincare.memLp_bump_convolution_compact","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.normed","ContinuousENorm.toENorm","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","GinibrePoincare.Configuration","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.convolution","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instDivisionRing","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.id","Bool","Bool.true","BorelSpace.opensMeasurable","Co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mplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreSymmetricWeakPoincare","name":"GinibrePoincare.memLp_centerOfMassImag","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassImag","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.abs_im_le_norm","Complex.borelSpace","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNorm","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","Continuous.pow","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DistribLattice.toLattice","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Filter.univ_mem'","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassImag","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","GinibrePoincare.coordinateSum_ginibre_gaussian","GinibrePoincare.ginibreMeasure","GinibrePoincare.integrable_norm_pow_complexCoordinateGaussianProbability","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.standardComplexGaussianMeasure","HPow.hPow","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.comp_aemeasurable","MeasureTheory.Integrable.mono'","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.memLp_two_iff_integrable_sq_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMonoid","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.instPow","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLE","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instPreorder","Real.instRCLike","Real.linearOrder","Real.metricSpace","Real.norm","Real.norm_of_nonneg","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomCompTriple.ids","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","True","UniformSpace.toTopologicalSpace","congrArg","continuous_norm","eq_self","funext","id","instCountableFin","instDistribLatticeOfLinearOrder","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","norm_nonneg","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper","sq_le_sq\u2080","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreSymmetricWeakPoincare","name":"GinibrePoincare.memLp_centerOfMassReal","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Complex","Complex.abs_re_le_norm","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instNorm","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Complex.re","Complex.reCLM","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","Continuous.pow","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DistribLattice.toLattice","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Filter.univ_mem'","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.coordinateSumCLM_apply","GinibrePoincare.coordinateSum_ginibre_gaussian","GinibrePoincare.ginibreMeasure","GinibrePoincare.integrable_norm_pow_complexCoordinateGaussianProbability","GinibrePoincare.measurable_coordinateSum","GinibrePoincare.standardComplexGaussianMeasure","HPow.hPow","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.comp_aemeasurable","MeasureTheory.Integrable.mono'","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.memLp_two_iff_integrable_sq_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMonoid","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","Pi.instPow","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLE","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instPreorder","Real.instRCLike","Real.linearOrder","Real.metricSpace","Real.norm","Real.norm_of_nonneg","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomCompTriple.ids","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","True","UniformSpace.toTopologicalSpace","congrArg","continuous_norm","eq_self","funext","id","instCountableFin","instDistribLatticeOfLinearOrder","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","norm_nonneg","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper","sq_le_sq\u2080","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.L2RepresentativeBridges","name":"GinibrePoincare.memLp_centeredObservable_of_core","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.centeredObservable","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","And","And.left","And.right","BorelSpace.opensMeasurable","BoundedContinuousFunction","BoundedContinuousFunction.instNorm","BoundedContinuousFunction.norm_coe_le_norm","Compl.compl","Complex","Complex.borelSpace","Complex.continuous_ofReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_sub","ContDiff","ContDiff.continuous","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENorm","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Filter.univ_mem'","Fin","Fin.fintype","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.centeredObservable","GinibrePoincare.collisionSet","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.smoothGinibreMean","HEq","HEq.refl","HSub.hSub","HasCompactSupport","HasCompactSupport.mono","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.of_bound","MeasureTheory.MemLp.sub","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.memLp_const","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLE","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompl","Set.instLE","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","Top.top","TopologicalSpace","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","autoParam","congrArg","congrFun'","eq_of_heq","eq_self","funext","id","instCountableFin","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","ofCompactSupport","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.memLp_configurationFourierCharacter","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationFourierCharacter","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Continuous.aestronglyMeasurable","EMetricSpace.toPseudoEMetricSpace","ENNReal","Eq.trans","Filter.Eventually.of_forall","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.continuous_configurationFourierCharacter","GinibrePoincare.instIsProbabilityMeasureComplexGaussianMeasure","GinibrePoincare.norm_configurationFourierCharacter","LE.le","MeasurableSpace.pi","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.of_bound","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Nat","Norm.norm","NormedAddCommGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instOne","Real.instPreorder","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Std.le_refl._simp_1","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","instCountableFin","instReflLe","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.memLp_configurationRealPairing","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationRealPairing","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instTop","ENNReal.ofNat_ne_top._simp_1","Eq","Eq.trans","False","GinibrePoincare.Configuration","GinibrePoincare.memLp_configurationRealPairing_of_ne_top","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Top.top","True","True.intro","congrArg","eq_false","eq_true","instOfNatAtLeastTwo","instOfNatNat","not_false","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialCompleteness","name":"GinibrePoincare.memLp_configurationRealPairing_of_ne_top","type_dependencies":["Complex","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.configurationRealPairing","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidHom","AddMonoidHom.instFunLike","AddSemigroup.toAdd","AddZero.mk","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommRing.toRing","Complex","Complex.borelSpace","Complex.im","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","Complex.re","ContinuousENorm.toENorm","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instTop","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","ESeminormedAddMonoid.toContinuousENorm","Eq","Eq.mpr","Eq.refl","Field.toCommRing","Fin","Fin.fintype","Finset","Finset.induction_on","Finset.instInsert","Finset.instSetLike","Finset.sum","Finset.sum_insert","Finset.univ","Function.eval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianProbability","GinibrePoincare.configurationRealPairing","GinibrePoincare.isGaussian_complexCoordinateGaussianProbability","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Insert.insert","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.add","MeasureTheory.MemLp.comp_measurePreserving","MeasureTheory.MemLp.const_mul","MeasureTheory.MemLp.im","MeasureTheory.MemLp.re","MeasureTheory.MemLp.zero'._simp_1","MeasureTheory.ProbabilityMeasure.instIsProbabilityMeasureToMeasure","MeasureTheory.ProbabilityMeasure.pi","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.measurePreserving_eval","Membership.mem","MetricSpace.toEMetricSpace","Nat","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedRing.toRing","NormedRing.toSeminormedRing","Not","OfNat.ofNat","Pi.instAdd","ProbabilityTheory.IsGaussian.memLp_id","PseudoMetricSpace.toUniformSpace","RCLike.im","RCLike.re","RCLike.toDenselyNormedField","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","SetLike.instMembership","Top.top","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.secondCountable_of_separable","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun'","funext","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","of_eq_true","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarCompactCore","name":"GinibrePoincare.memLp_coordinate_mul_finiteHermiteFunction","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instMul","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteFunction","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENormedAddCommMonoid.toESeminormedAddCommMonoid","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_apply","Finset.sum_congr","Finsupp","Finsupp.instFunLike","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteFunction","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.memLp_two_coordinate_mul_multivariateNormalized","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.MemLp","MeasureTheory.MemLp.const_mul","MeasureTheory.memLp_finsetSum","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun","congrFun'","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorWeakCore","name":"GinibrePoincare.memLp_coreObservable","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","And","And.left","And.right","BorelSpace.opensMeasurable","Compl.compl","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.continuous_ofReal","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_zero","ContDiff","ContDiff.continuous","Continuous.comp","Continuous.memLp_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","Finite.of_fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","HasCompactSupport","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instCompl","Set.instLE","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","WithTop.some","instCountableFin","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSigmaCompactSpaceForallOfFinite","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","secondCountable_of_proper","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.memLp_dbarComponent","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.dbarComponent","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","ContDiff","Continuous.memLp_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","Finite.of_fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.continuous_dbarComponent","GinibrePoincare.dbarComponent","GinibrePoincare.hasCompactSupport_dbarComponent","GinibrePoincare.instIsProbabilityMeasureComplexGaussianMeasure","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instCountableFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSigmaCompactSpaceForallOfFinite","locallyCompact_of_proper","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGeneratorL2","name":"GinibrePoincare.memLp_ginibrePregenerator_of_core","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.left","And.right","BorelSpace.opensMeasurable","Compl.compl","Complex","Complex.borelSpace","Complex.continuous_ofReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiff","Continuous.comp","Continuous.memLp_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.trans","Fin","Fin.fintype","Finite.of_fintype","Function.comp","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.continuous_ginibrePregenerator_of_core","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.ginibrePregenerator","GinibrePoincare.hasCompactSupport_ginibrePregenerator","HasCompactSupport","HasCompactSupport.mono","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompl","Set.instLE","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","TopologicalSpace.pseudoMetrizableSpace_pi","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","congrFun'","eq_self","instCountableFin","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSigmaCompactSpaceForallOfFinite","instTopENat","locallyCompact_of_proper","of_eq_true","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDensityBound","name":"GinibrePoincare.memLp_ginibre_of_volume","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","And","And.casesOn","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousENorm.toENorm","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instTop","Exists","Exists.casesOn","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_le_finite_smul_volume","HSMul.hSMul","IsScalarTower.right","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instPartialOrder","MeasureTheory.Measure.instSMul","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.of_measure_le_smul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorWeakCore","name":"GinibrePoincare.memLp_polynomialEigenfunction_generator","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.complexGinibrePregenerator","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunction","LE.le","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCancelMonoid.toAddRightCancelMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddRightCancelMonoid.toAddRightCancelSemigroup","AddRightCancelSemigroup.toIsRightCancelAdd","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instCommSemiring","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_add","Complex.ofReal_mul","ContinuousENorm.toENorm","Distrib.toAdd","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.PolynomialEigenfunctionData.mk","GinibrePoincare.complexGinibrePregenerator","GinibrePoincare.eigenvalue","GinibrePoincare.eigenvalueAtSpeed._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunction_eigenvalue_equation_ae","GinibrePoincare.polynomialEigenfunction_memLp_two","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LE.le","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.ae_eq","MeasureTheory.MemLp.const_mul","MeasureTheory.ae","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instMul","Real.instNatCast","Ring","Ring.toAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialL2Convolution","name":"GinibrePoincare.memLp_radial_convolution_compact","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierKernel","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.convolution","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instSub","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.id","And","And.left","And.right","Bool","Bool.true","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instT2Space","Complex.measurableSpace","ContDiff","ContDiff.continuous","Continuous.memLp_of_hasCompactSupport","ContinuousAdd.measurableAdd","ContinuousENorm.toENorm","ContinuousLinearMap.lsmul","ContinuousNeg.measurableNeg","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","ENat","Eq","Eq.refl","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierKernel","GinibrePoincare.radialMollifierKernel_properties","HasCompactSupport","HasCompactSupport.contDiff_convolution_left","HasCompactSupport.convolution","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite"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stLE","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.inv_mul_cancel","ENNReal.inv_ne_top","ENNReal.ofReal","ENNReal.ofReal_le_ofReal","ENNReal.ofReal_ne_top","ENNReal.ofReal_pos","Eq","Eq.mp","Eq.mpr","Eq.symm","Eq.trans","Filter.mp_mem","Filter.univ_mem'","HMul.hMul","HSMul.hSMul","Iff.mpr","Inv.inv","IsScalarTower.left","IsScalarTower.right","LE.le","LT.lt","LT.lt.ne'","MeasurableSet","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instPartialOrder","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.restrict","MeasureTheory.Measure.withDensity","MeasureTheory.MemLp","MeasureTheory.MemLp.mono_measure","MeasureTheory.MemLp.restrict","MeasureTheory.MemLp.smul_measure","MeasureTheory.ae","MeasureTheory.ae_restrict_mem","MeasureTheory.restrict_withDensity","MeasureTheory.withDensity_const","MeasureTheory.withDensity_mono","Membership.mem","Monoid.toMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SemigroupAction.toSMul","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instDistribOfSemiring","instHMul","instHSMul","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","one_smul","smul_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreGeneratorL2","name":"GinibrePoincare.memLp_shiftedGinibrePregenerator_of_core","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePregenerator","HAdd.hAdd","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAdd","Real.instMul","Real.instNatCast","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHAdd","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And","And.left","And.right","BorelSpace.opensMeasurable","Compl.compl","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.continuous_ofReal","Complex.instAdd","Complex.instCompleteSpace","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_add","Complex.ofReal_mul","ContDiff","ContDiff.continuous","Continuous.comp","Continuous.memLp_of_hasCompactSupport","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENorm","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","ESeminormedAddMonoid.toContinuousENorm","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Fin","Fin.fintype","Finite.of_fintype","Function.comp","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.collisionSet","GinibrePoincare.ginibreMeasur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ddMonoidWithOne.toNatCast","And","And.left","And.right","BorelSpace.opensMeasurable","BoundedContinuousFunction","BoundedContinuousFunction.instNorm","BoundedContinuousFunction.norm_coe_le_norm","Complex","Complex.borelSpace","Complex.continuous_ofReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_sub","ContDiff","ContDiff.continuous","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENorm","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Filter.univ_mem'","Fin","Fin.fintype","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.IsSymmetric","GinibrePoincare.centeredObservable","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","GinibrePoincare.smoothGinibreMean","HEq","HEq.refl","HSub.hSub","HasCompactSupport","HasCompactSupport.mono","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.of_bound","MeasureTheory.MemLp.sub","MeasureTheory.ae","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.memLp_const","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toPseudoMetricSpace","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLE","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","Top.top","TopologicalSpace","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","autoParam","congrArg","congrFun'","eq_of_heq","eq_self","funext","id","instCountableFin","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instTopENat","ofCompactSupport","of_eq_true","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.memLp_two_coordinate_mul_multivariateNormalized","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instMul","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","HMul.hMul","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAdd","AddMonoid.toAddZeroClass","AddMonoid.toZero","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne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Ring","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.ofPred","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.subset_span","Subtype","UniformSpace.toTopologicalSpace","instHMul","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRadialCompactWeakGradient","name":"GinibrePoincare.memLp_two_volume_of_compact_support_restrict","type_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","tsupport"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENormedAddMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.trans","False","Fin","Fin.fintype","GinibrePoincare.Configuration","HPow.hPow","Iff.mp","Iff.mpr","MeasurableSpace.pi","MeasureTheory.AEStronglyMeasurable","MeasureTheory.Integrable","MeasureTheory.IntegrableOn","MeasureTheory.IntegrableOn.integrable_of_forall_notMem_eq_zero","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.aestronglyMeasurable","MeasureTheory.memLp_two_iff_integrable_sq_norm","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instMonoidWithZero","Real.instZero","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","image_eq_zero_of_notMem_tsupport","instHPow","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","norm_zero","not_false_eq_true","of_eq_true","tsupport","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Concrete.Configuration","name":"GinibrePoincare.mem_collisionSet_iff","type_dependencies":["And","Complex","Eq","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","Iff","Membership.mem","Nat","Ne","Set","Set.instMembership"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.collisionSet","Iff.rfl","Membership.mem","Nat","Set","Set.instMembership"]},{"kind":"theorem","module":"GinibrePoincare.Concrete.Configuration","name":"GinibrePoincare.mem_collisionSet_iff._simp_1","type_dependencies":["And","Complex","Eq","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","Membership.mem","Nat","Ne","Set","Set.instMembership"],"value_dependencies":["And","Complex","Eq","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.collisionSet","GinibrePoincare.mem_collisionSet_iff","Membership.mem","Nat","Ne","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireRepresentatives","name":"GinibrePoincare.mem_gaussianEntireL2_iff","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNontriviallyNormedField","Differentiable","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists","Field.toDivisionRing","Field.toSemifield","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireL2","Iff","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireL2","Iff.rfl","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarEqualitySpace","name":"GinibrePoincare.mem_gaussianGapEqualitySpace_iff","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianGapEqualitySpace","GinibrePoincare.gaussianHermiteMode","Iff","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","A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f","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianWeakClosedFormSpace","Iff.rfl","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianClosedFormSolvability","name":"GinibrePoincare.mem_gaussianWeakClosedFormSpace._simp_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsGaussianWeakClosedForm","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianWeakClosedFormSpace","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommM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iteSpan._proof_2","GinibrePoincare.gaussianHermiteSpan._proof_4","GinibrePoincare.gaussianHermiteSpan._proof_5","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.multivariateNormalizedL2._proof_1","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Set.range","SetLike.instMembership","Submodule.subset_span","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryTensorExpansion","name":"GinibrePoincare.multivariateNormalizedL2_tensor_expansion","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","Fin.fintype","Fin.val","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.TensorHermiteContraction","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.multivariateMixedMonomialL2","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.tensorHermiteScalar","GinibrePoincare.tensorHermiteScale","HAdd.hAdd","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Min.min","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instFintype","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instAddNat","instDecidableEqFin","instHAdd","instHSMul","instHSub","instLTNat","instMinNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","C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mpr","Eq.rec","Eq.refl","Eq.symm","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.univ","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.coordinate_normalizedEval_matrix_element","GinibrePoincare.integral_normalizedEval_mul_conj_normalizedEval","GinibrePoincare.multivariate_coordinate_matrix_element_factorization","HAdd.hAdd","HMul","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","Real","Real.instNatCast","Real.instRCLike","Real.sqrt","RingHom","RingHom.instFunLike","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Zero.toOfNat0","congrArg","id","instDecidableAnd","instDecidableEqFin","instDecidableEqNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instSubNat","ite","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianDbarParseval","name":"GinibrePoincare.multivariate_coordinate_matrix_element_factorization","type_dependencies":["CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","Eq","Fin","Fin.fintype","Finset.erase","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","MeasurableSpace.pi","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.integral","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Real","Real.instRCLike","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instDecidableEqFin","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","And","And.right","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toCommRing","Fin","Fin.fintype","Finset","Finset.erase","Finset.erase_eq","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_sdiff","Finset.mem_singleton._simp_1","Finset.mem_univ._simp_1","Finset.prod","Finset.prod_congr","Finset.prod_eq_mul_prod_diff_singleton","Finset.prod_mul_distrib","Finset.univ","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianProbability","HAdd.hAdd","HMul","HMul.hMul","HPow.hPow","Iff.mp","InnerProductSpace.toNormedSpace","IsEmpty.forall_iff._simp_1","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.atom_pf'","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Co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"instInhabitedNat","instIsDirectedOrder","instNonemptyOfInhabited","instOrderTopologyReal","nhds","tendsto_order"]},{"kind":"definition","module":"GinibrePoincare.Endgame.HilbertGeometry","name":"GinibrePoincare.normSq","type_dependencies":["Norm","Real"],"value_dependencies":["HMul.hMul","Norm","Norm.norm","Real","Real.instMul","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.HilbertGeometry","name":"GinibrePoincare.normSq.eq_1","type_dependencies":["Eq","GinibrePoincare.normSq","HMul.hMul","Norm","Norm.norm","Real","Real.instMul","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.normSq","Norm","Real"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.HilbertGeometry","name":"GinibrePoincare.normSq_add_of_inner_eq_zero","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Eq","Field.toSemifield","GinibrePoincare.normSq","HAdd.hAdd","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","MulZeroClass.toZero","NormedField.toField","OfNat.ofNat","RCLike","RCLike.toDenselyNormedField","Real","Real.instAdd","Semifield.toCommSemiring","SeminormedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","Zero.toOfNat0","instHAdd","instMulZeroClassOfSemiring"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","CommSemiring.toSemiring","DenselyNormedField.toNormedField","Eq","Field.toSemifield","GinibrePoincare.normSq","HAdd.hAdd","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","MulZeroClass.toZero","NormedField.toField","OfNat.ofNat","RCLike","RCLike.toDenselyNormedField","Real","Real.instAdd","Semifield.toCommSemiring","SeminormedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","Zero.toOfNat0","id","instHAdd","instMulZeroClassOfSemiring","norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.normSq_dbarComponent_ofReal","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DivInvMonoid.toDiv","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.div_ofNat_im","Complex.div_ofNat_re","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.mul_im","Complex.mul_re","Complex.normSq","Complex.ofReal","Complex.re","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDi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nLike.coe","ENNReal.toReal","ENNReal.toReal_nonneg","Eq","Eq.mpr","Eq.refl","Eq.symm","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.groundStateNormalization","HMul.hMul","HPow.hPow","Inv.inv","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","Real","Real.instInv","Real.instMonoid","Real.instMul","Real.semiring","Real.sq_sqrt","Real.sqrt","congrArg","id","instHMul","instHPow","instMulZeroOneClassOfSemiring","instOfNatNat","pow_two"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.HilbertGeometry","name":"GinibrePoincare.normSq_map_linearIsometryEquiv","type_dependencies":["CommSemiring.toSemiring","DFunLike.coe","DenselyNormedField.toNormedField","Eq","EquivLike.toFunLike","Field.toSemifield","GinibrePoincare.normSq","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","NormedField.toField","NormedSpace","NormedSpace.toModule","RCLike","RCLike.toDenselyNormedField","Real","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup","SeminormedAddCommGroup.toNorm","Semiring.toNonAssocSemiring"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddZeroClass.toAddZero","CommSemiring.toSemiring","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.trans","EquivLike.toFunLike","Field.toSemifield","GinibrePoincare.normSq","HMul.hMul","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.instSemilinearIsometryEquivClass","Module.toDistribMulAction","Norm.norm","NormedField.toField","NormedSpace","NormedSpace.toModule","RCLike","RCLike.toDenselyNormedField","Real","Real.instMul","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","Semifield.toCommSemiring","SemilinearIsometryClass.toIsometryClass","SemilinearIsometryClass.toSemilinearMapClass","SemilinearIsometryEquivClass.toSemilinearIsometryClass","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","Semiring.toMonoid","Semiring.toNonAssocSemiring","True","congr","congrArg","congrFun'","eq_self","instHMul","norm_map","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.HilbertGeometry","name":"GinibrePoincare.normSq_nonneg","type_dependencies":["GinibrePoincare.normSq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","SeminormedAddCommGroup","SeminormedAddCommGroup.toNorm","Zero.toOfNat0"],"value_dependencies":["AddGroup.existsAddOfLE","DistribLattice.toLattice","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","Lattice.toSemilatticeInf","Norm.norm","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instPreorder","Real.linearOrder","Real.partialOrder","Real.semiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup","SeminormedAddCommGroup.toNorm","instDistribLatticeOfLinearOrder","mul_self_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.normSq_normalizedVandermondeTransform","type_dependencies":["Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","ENNReal.toReal","Eq","GinibrePoincare.Configuration","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.vandermondeWeight","HMul.hMul","Inv.inv","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Real","Real.instInv","Real.instMul","Real.semiring","instHMul","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.instInv","Complex.instMul","Complex.instSemiring","Complex.normSq","Complex.normSq_mul","Complex.ofReal","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal.toReal","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.groundStateNormalization","GinibrePoincare.normSq_groundStateNormalization_inv","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.normalizedVandermondeTransform_apply","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeWeight","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Met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GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne"],"value_dependencies":["Complex","Complex.instNorm","Complex.norm_exp_ofReal_mul_I","Eq","GinibrePoincare.Configuration","GinibrePoincare.configurationFourierCharacter","GinibrePoincare.configurationRealPairing","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDifferentiability","name":"GinibrePoincare.norm_fderiv_fintype_prod_le","type_dependencies":["AddCommGroup.toAddCommMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instNorm","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Field.toSemifield","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","HMul.hMul","LE.le","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instCommMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instZero","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommMonoidWithZero.toCommMonoid","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instSMul","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.erase","Finset.instSetLike","Finset.mem_univ","Finset.prod","Finset.prod_erase_mul","Finset.prod_le_prod\u2080","Finset.prod_nonneg","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.univ","Fintype.card_fin","GinibrePoincare.Configuration","HMul.hMul","HSMul.hSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","NSMul.toSMul","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_isTopologicalDivisionRing","NormedDivisionRing.to_normOneClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","Pi.Function.module","Pi.addCom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","pow_pos","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.LipschitzMollification","name":"GinibrePoincare.norm_fderiv_mollification_le","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.normed","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","EMetricSpace.toPseudoEMetricSpace","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","FiniteDimensional","InnerProductSpace.toNormedSpace","IsScalarTower.right","LE.le","LipschitzWith","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.convolution","MetricSpace.toEMetricSpace","NNReal","NNReal.toReal","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivisionRing","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","Algebra.to_smulCommClass","BorelSpace","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.continuous","ContDiffBump","ContDiffBump.contDiff_normed","ContDiffBump.hasCompactSupport_normed","ContDiffBump.integral_normed","ContDiffBump.nonneg_normed","ContDiffBump.normed","Continuous.integrable_of_hasCompactSupport","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instSMul","ContinuousLinearMap.isScalarTower","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toNormedSpace._proof_1","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","ENat","Eq","Eq.mpr","Eq.refl","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually.of_forall","FiniteDimensional","FiniteDimensional.proper_real","GinibrePoincare.fderiv_normed_convolution_lipschitz","HMul.hMul","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LipschitzWith","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_const","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.integral","MeasureTheory.integral_mono_of_nonneg","MeasureTheory.integral_mul_const","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.norm_integral_le_integral_norm","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulAction","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toSMulWithZero","MulZeroOneClass.toMulOneClass","NNReal","NNReal.toReal","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instZero","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.lattice","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","Trans.trans","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","fderiv","id","instClosedIciTopology","instDistribOfSemiring","instHMul","instHSMul","instHSub","instHasSolidNormReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instSMulCommClassOfIsScalarTower","instTopENat","instTransEq_1","instTransLE","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","mul_le_mul_of_nonneg_left","norm_fderiv_le_of_lipschitz","norm_nonneg","norm_smul","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireDifferentiability","name":"GinibrePoincare.norm_fderiv_normalized_coordinate_pow_le","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instMul","Complex.instNorm","Complex.instNormedField","Complex.instSemiring","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","Ad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OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instPow","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","PolynormableSpace.continuousSMul","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_nonneg","Real.sqrt_pos_of_pos","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNorm","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","cast","congrArg","differentiable_apply","fderiv","fderiv_const_mul","fderiv_pow","hasFDerivAt_apply","id","inferInstance","instContinuousSMulForall","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNatPowNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instPowNat","instSMulCommClassOfIsScalarTower","instSubNat","instTransEq","instTransEq_1","le_of_lt","lt_of_lt_of_le","mul_le_mul","mul_le_mul_of_nonneg_left","mul_nonneg","mul_one","mul_pos","mul_pow","norm_le_pi_norm","norm_mul","norm_nonneg","norm_pow","norm_smul","nsmul_eq_mul","one_mul","pow_le_pow_left\u2080","pow_le_pow_right\u2080","pow_nonneg","pow_pos","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianEntireSeriesBounds","name":"GinibrePoincare.norm_holomorphicHermite_le_tensor_bound","type_dependencies":["Complex","Complex.instNorm","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","HMul.hMul","HPow.hPow","LE.le","LT.lt","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instMulZeroClass","Norm.norm","OfNat.ofNat","Pi.instZero","Real","Real.instCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instZero","Zero.toOfNat0","instHMul","instHPow","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instMul","Complex.instNorm","Complex.instNormedField","Complex.instSemiring","Complex.norm_real","Complex.ofReal","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.prod_le_prod\u2080","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.multivariateNormalized_zero_right","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","Membership.mem","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Nat.factorial","Nat.factorial_pos","Nat.instMulZeroClass","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedDivisionRing.to_normOneClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Pi.instZero","PosMulReflectLE.toPosMulReflectLT"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onoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.centeredObservableL2","GinibrePoincare.centeredObservableL2._proof_1","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","GinibrePoincare.norm_sq_centeredObservableL2","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.smoothGinibreVariance","GinibrePoincare.transformedCenteredObservableL2","GinibrePoincare.transformedCenteredObservableL2._proof_1","GinibrePoincare.transformedCenteredObservableL2._proof_2","GinibrePoincare.transformedCenteredObservableL2.eq_1","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.norm_map","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BernoulliGaussianCLT","name":"GinibrePoincare.normalizedBernoulliSum","type_dependencies":["Nat","Real"],"value_dependencies":["Finset.range","Finset.sum","HMul.hMul","Inv.inv","Nat","Nat.cast","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.sqrt","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BernoulliTaylorEnergy","name":"GinibrePoincare.normalizedBernoulliSum.eq_1","type_dependencies":["Eq","Finset.range","Finset.sum","GinibrePoincare.normalizedBernoulliSum","HMul.hMul","Inv.inv","Nat","Nat.cast","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","Real.sqrt","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.normalizedBernoulliSum","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BernoulliGaussianCLT","name":"GinibrePoincare.normalizedBernoulliSum_clt","type_dependencies":["BorelSpace.opensMeasurable","Filter.atTop","GinibrePoincare.normalizedBernoulliSum","GinibrePoincare.rademacherProduct","GinibrePoincare.rademacherProduct_probability","MeasurableSpace.pi","MeasureTheory.TendstoInDistribution","NNReal","NNReal.instOne","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gaussianReal","ProbabilityTheory.instIsProbabilityMeasureGaussianReal","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.instZero","Real.measurableSpace","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","id"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace.opensMeasurable","CharZero.NeZero.two","CommRing.toNonUnitalCommRing","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.rademacherCoordinate_hasLaw","GinibrePoincare.rademacherMeasure","GinibrePoincare.rademacher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edCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_1","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.instNormedAddCommGroup","ContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup.toContinuousAdd","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_1","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_1","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_5","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_7","GinibrePoincare.normalizedPolynomialSectorEigenvector._proof_8","IsScalarTower","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instSMulOfMul"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.Lp.instIsScalarTower","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","RCLike.innerProductSpace","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","instOfNatAtLeastTwo","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisi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SectorEigenvector","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorEigenvector_mem_normalized_span","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","MulZeroClass.toZero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.range","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.instOrderTop","Submodule.instPartialOrder","Submodule.isClosed_topologicalClosure","Submodule.isTopologicalAddGroup","Submodule.le_topologicalClosure","Submodule.module","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smul_mem","Submodule.span","Submodule.sum_mem","Submodule.topologicalClosure","Submodule.zero","Subtype","Subtype.pseudoMetricSpace","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHSMul","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","instUniformSpaceSubtype","top_unique"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorHilbertBasis","name":"GinibrePoincare.normalizedPolynomialSectorEigenvector_orthonormal","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedPolynomialSectorEigenvector","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Nor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ateL2._proof_6","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.normalizedVandermondeGroundStateL2._proof_2","GinibrePoincare.polynomialVandermonde","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Exists.choose","Field.toDivisionRing","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.exists_memLp_configurationPolynomial_mem_antiDegreeZeroSpan","GinibrePoincare.polynomialVandermonde","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.MemLp","MeasureTheory.MemLp.toLp","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","name":"GinibrePoincare.normalizedVandermondeGroundStateL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.normalizedVandermondeGroundStateL2","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup",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onde","HMul.hMul","Inv.inv","Nat","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","name":"GinibrePoincare.normalizedVandermondeMultiplier.eq_1","type_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.ofReal","Eq","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.vandermonde","HMul.hMul","Inv.inv","Nat","instHMul"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.normalizedVandermondeMultiplier","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_mem_gaussianAlternating","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_1","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_10","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_2","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_3","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_4","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_5","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_7","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_8","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_9","LT.lt","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.mk","LinearMap.mk","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedA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ometryClass","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SemilinearIsometryClass.toSemilinearMapClass","SemilinearMapClass.toAddHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.ext","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHAdd","instLTNat","instOfNatAtLeastTwo","instOfNatNat","map_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2._proof_10","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_3","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_4","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_5","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_7","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_8","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry.norm_map","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAs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.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_3","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_6","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_3","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_6","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2EquivRange","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeSymmetricL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry.toLinearMap","LinearIsometryEquiv","LinearMap.range","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","RingHomSurjective.invPair","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeSymmetricL2","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_3","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_4","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_5","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_7","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_8","GinibrePoincare.normalizedVandermondeSymmetricL2._proof_9","GinibrePoincare.normalizedVandermondeSymmetricL2EquivRange._proof_1","LT.lt","LinearIsometry.equivRange","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.VandermondeSymmetryL2","name":"GinibrePoincare.normalizedVandermondeSymmetricL2EquivRange._proof_1","type_dependencies":["Complex","Complex.instRing","Ring.toSemiring","RingHom.id","RingHomInvPair","Semiring.toNonAssocSemiring"],"value_dependencies":["Complex","Complex.instRing","Ring.toSemiring","RingHomInvPair.ids"]},{"kind":"definition","module":"GinibrePoincare.Concrete.NormalizedGroundState","name":"GinibrePoincare.normalizedVandermondeTransform","type_dependencies":["Complex","GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.ofReal","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.vandermondeTransform","HMul.hMul","Inv.inv","Nat","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionEndpoints","name":"GinibrePoincare.normalizedVandermondeTransform.eq_1","type_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.ofReal","Eq","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.vandermondeTransform","HMul.hMul","Inv.inv","Nat","instHMul"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.normalizedVandermondeTransform","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Concrete.NormalizedGroundState","name":"GinibrePoincare.normalizedVandermondeTransform_apply","type_dependencies":["Complex","Complex.instInv","Complex.instMul","Complex.ofReal","Eq","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.vandermonde","HMul.hMul","Inv.inv","Nat","instHMul"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.ofReal","Distrib.toAdd","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.Configuration","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeTransform","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Concrete.NormalizedGroundState","name":"GinibrePoincare.normalizedVandermondeTransform_isAlternating","type_dependencies":["Complex","GinibrePoincare.Configuration","GinibrePoincare.IsAlternating","GinibrePoincare.IsSymmetric","GinibrePoincare.normalizedVandermondeTransform","Nat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.ofReal","Distrib.toAdd","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.ParticlePermutation","GinibrePoincare.groundStateNormalization","GinibrePoincare.normalizedVandermondeTransform","GinibrePoincare.permutationSign","GinibrePoincare.permute","GinibrePoincare.vandermondeTransform","GinibrePoincare.vandermondeTransform_isAlternating","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congrArg","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianGinibreProjectionIntertwining","name":"GinibrePoincare.normalizedVandermonde_entire_infDist","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireClosedSpace","GinibrePoincare.ginibreDivisibleEntireClosedSpace","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Metric.infDist","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.closedSubspace_infDist_eq_projectionNorm","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianEntireClosedSpace","GinibrePoincare.ginibreDivisibleEntireClosedSpace","GinibrePoincare.ginibreDivisibleEntireClosedSpace_eq_holomorphic","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermonde_projection_distance","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Metric.infDist","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instMonoid","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.coe","SetLike.instMembership","SubNegMonoid.toSub","Submodule","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.setLike","Submodule.starProjection","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHPow","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianGinibreProjectionIntertwining","name":"GinibrePoincare.normalizedVandermonde_holomorphicAmbient_mem_zeroMode","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","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llyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.to_smulCommClass","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousAdd.measurableAdd","ContinuousLinearMap.mul","ContinuousNeg.measurableNeg","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","HasCompactSupport","HasCompactSupport.contDiff_convolution_left","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.Pi.isAddLeftInvariant_volume","MeasureTheory.Pi.isNegInvariant_volume","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MetricSpace.toEMetricSpace","Nat","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","instCountableFin","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultMollification","name":"GinibrePoincare.ordinaryDolbeaultMollify_dbar","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.ordinaryDolbeaultMollify","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.instT2Space","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous_fderiv","Continuous","Continuous.clm_apply","Continuous.comp","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.ordinaryDolbeaultMollify","GinibrePoincare.ordinaryDolbeaultMollify_directional","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_homeomorph","HasCompactSupport.fderiv_apply","Homeomorph.subLeft","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsTopologicalAddGroup.to_continuousSub","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasureTheory.Integrable","MeasureTheory.Integrable.const_mul","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.integral_add","MeasureTheory.integral_const_mul","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.addGroup","Pi.instSub","Pi.isTopologicalAddGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.seminormedAddCommGroup","Pi.t2Space","Pi.topologicalSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","continuous_const","continuous_id","fderiv","funext","id","instCountableFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","instZeroENat","measureSpaceOfInnerProductSpace","not_false_eq_true","of_eq_true","rfl","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultMollification","name":"GinibrePoincare.ordinaryDolbeaultMollify_directional","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ordinaryDolbeaultMollify","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toRing",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Mul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","congrArg","eq_self","fderiv","id","instContinuousSMulForall","instCountableFin","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instOneENat","instOrderTopENat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instPolynormableSpace","instPreorderENat","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","not_false_eq_true","of_eq_true","rfl","secondCountable_of_proper","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultApproximation","name":"GinibrePoincare.ordinaryDolbeaultPiMollification_closed_ball","type_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiffBump","ContDiffBump.rOut","ContinuousENorm.toENorm","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DistribMulAction.toMulAction","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.piPlanarBump","HAdd.hAdd","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","LE.le","LT.lt","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.convolution","MeasureTheory.integral","Metric.ball","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instLT","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instTopENat","measureSpaceOfInnerProductSpace","pseudoMetricSpacePi","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","Bool","Bool.true","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Comple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CompactWeightedDbarGraph._proof_2","type_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Fin","GinibrePoincare.Configuration","GinibrePoincare.piPotentialHalfWeight","HAdd.hAdd","HMul.hMul","HasCompactSupport","MulZeroClass.toMul","MulZeroClass.toZero","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instMulZeroClassOfSemiring","instOfNatNat"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Fin","GinibrePoincare.Configuration","GinibrePoincare.piPotentialHalfWeight","HAdd.hAdd","HasCompactSupport","HasCompactSupport.mul_right","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instMulZeroClassOfSemiring","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiCompactGraphApproximation","name":"GinibrePoincare.piCompactWeightedDbarGraph._proof_3","type_dependencies":["Complex","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.piComplexDbar","GinibrePoincare.piPotentialHalfWeight","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.instMul","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instAddNat","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatNat","instOneENat"],"value_dependencies":["Complex","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","Continuous.mul","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.piComplexDbar","GinibrePoincare.piComplexDbar_continuous","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.piPotentialHalfWeight_continuous","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.pseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiCompactGraphApproximation","name":"GinibrePoincare.piCompactWeightedDbarGraph._proof_4","type_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Fin","GinibrePoincare.Configuration","GinibrePoincare.piComplexDbar","GinibrePoincare.piPotentialHalfWeight","HAdd.hAdd","HMul.hMul","HasCompactSupport","MulZeroClass.toMul","MulZeroClass.toZero","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instHMul","instMulZeroClassOfSemiring","instOfNatNat"],"value_dependencies"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inibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.piCompactWeightedDbarGraph","GinibrePoincare.planarPiCompactGraphAverage","GinibrePoincare.planarPiCompactGraphAverage_mem","GinibrePoincare.planarPiCompactGraphAverage_tendsto","GinibrePoincare.planarPiDbarGraphMap","GinibrePoincare.planarPiShrinkingBump","GinibrePoincare.planarPiShrinkingBump_rOut_tendsto","HAdd.hAdd","HasCompactSupport","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsClosed.mem_of_tendsto","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap.range","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Nat.instCommSemiring","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.continuousAdd'","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod.continuousAdd","Prod.continuousConstSMul","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","RingHomSurjective.ids","SemigroupAction.toSMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","Submodule","Submodule.isClosed_topologicalClosure","Submodule.setLike","Submodule.topologicalClosure","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fact_one_le_two_ennreal","instAddNat","instArchimedeanNat","instContinuousConstSMulForall","instHAdd","instInhabitedNat","instInnerProductSpaceRealComplex","instIsDirectedOrder","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instTopologicalSpaceProd","measureSpaceOfInnerProductSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPiSeparatedDerivatives","name":"GinibrePoincare.piComplexDbar","type_dependencies":["Complex","Fin","GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.I","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instZero","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.finiteComplexDbar","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.single","Real","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","instDecidableEqFin","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialVandermondeGauge","name":"GinibrePoincare.piComplexDbar.eq_1","type_dependencies":["Complex","Complex.I","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instZero","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.finiteComplexDbar","GinibrePoincare.piComplexDbar","InnerProductSpace.toNormedSpace","Nat","NonUnitalS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Mul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_zero","ContDiffBump","Continuous","Continuous.comp","Continuous.mul","Continuous.sub","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.finiteDimensionalL2_kernel_integral_ae","GinibrePoincare.finiteTranslatedKernel_hasCompactSupport","GinibrePoincare.integrable_piL2BumpIntegrand","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.piCompactFunctionL2","GinibrePoincare.piL2BumpAverage","GinibrePoincare.piPlanarBump","GinibrePoincare.piPlanarBump_compact","GinibrePoincare.piPlanarBump_continuous","GinibrePoincare.piTranslate_compact_smul_ae","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsLocallyFiniteMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.addGroup","Pi.borelSpace","Pi.complete","Pi.instSub","Pi.isTopologicalAddGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_fst","continuous_snd","fact_one_le_two_ennreal","id","instCountableFin","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiBumpAverage","name":"GinibrePoincare.piL2BumpAverage_error_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","CompleteSpace","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.support","GinibrePoincare.Configuration","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.piL2BumpAverage","GinibrePoincare.piPlanarBump","HSub.hSub","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.normedField","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.support","GinibrePoincare.Configuration","GinibrePoincare.integrable_piL2BumpIntegrand","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.piL2BumpAverage","GinibrePoincare.piL2BumpAverage._proof_1","GinibrePoincare.piL2BumpAverage._proof_2","GinibrePoincare.piL2BumpAverage._proof_3","GinibrePoincare.piL2BumpAverage._proof_4","GinibrePoincare.piL2BumpAverage._proof_5","GinibrePoincare.piPlanarBump","GinibrePoincare.piPlanarBump_integrable","GinibrePoincare.piPlanarBump_integral","GinibrePoincare.piPlanarBump_nonneg","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsTopologicalAddGroup.toContinuousAdd","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_const","MeasureTheory.Integrable.smul_const","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_mul_const","MeasureTheory.integral_sub","MeasureTheory.norm_integral_le_of_norm_le","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSM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WithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instCountableFin","instDecidableEqFin","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOneENat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSeparatelyContinuousAddOfContinuousAdd","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiSeparatedDerivatives","name":"GinibrePoincare.piSeparated_fderiv_single","type_dependencies":["AddCommGroup.toAddCommMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.erase","Finset.prod","Finset.univ","GinibrePoincare.Configuration","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.single","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instDecidableEqFin","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.commRing","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instT2Space","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.smul_apply","ContinuousLinearMap.sum_apply","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.prod","Finset.prod_congr","Finset.sum","Finset.sum_congr","Finset.sum_eq_single","Finset.univ","Function.comp","GinibrePoincare.Configuration","HMul.hMul","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","HasFDerivAt.finsetProd","InnerProductSpace.toNormedSpace","IsEmpty.forall_iff._simp_1","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSemi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tNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","BorelSpace.opensMeasurable","Complex","Complex.SMul.instSMulRealComplex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.real_smul","Continuous","Continuous.memLp_of_hasCompactSupport","ContinuousAdd.measurableAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.lebesgueL2Translate","GinibrePoincare.lebesgueL2Translate_ae","GinibrePoincare.piCompactFunctionL2","GinibrePoincare.piCompactFunctionL2._proof_1","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.IsAddLeftInvariant.isAddRightInvariant","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsAddRightInvariantForallVolumeOfMeasurableAddOfSigmaFinite","MeasureTheory.Measure.instIsFiniteMeasureOnCompactsForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.ae","MeasureTheory.eventually_add_right_iff","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.addGroup","Pi.instNeg","Pi.instSub","Pi.measurableAdd","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toMonoid","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","congrArg","id","instCountableFin","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSeparatelyContinuousAddOfContinuousAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ProductWeightedMeasure","name":"GinibrePoincare.pi_withDensity_ofReal_eq","type_dependencies":["ENNReal.ofReal","Eq","Finset.prod","Finset.univ","Fintype","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","MeasureTheory.SigmaFinite","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instCommMonoid","Real.instLE","Real.instZero","Real.measurableSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CommMonoid","CommRing.toCommMonoid","CommSemiring.toCommMonoid","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_prod_of_nonneg","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toCommRing","Finite.of_fintype","Finite.to_countable","Finset","Finset.instSetLike","Finset.prod","Finset.prod_nonneg","Finset.univ","Fintype","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedRing.toPosMulMono","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","LE.le","Measurable","MeasurableSet","MeasurableSet.univ_pi","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.fintype_prod","MeasureTheory.Integrable.restrict","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi_eq","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_pi_pi","MeasureTheory.Measure.withDensity","MeasureTheory.Restrict.sigmaFinite","MeasureTheory.SigmaFinite","MeasureTheory.ae_of_all","MeasureTheory.integral","MeasureTheory.integral_fintype_prod_eq_prod","MeasureTheory.integral_nonneg","MeasureTheory.lintegral","MeasureTheory.ofReal_integral_eq_lintegral_ofReal","MeasureTheory.withDensity_apply","Membership.mem","MulZeroClass.toSMulWithZero","NegZeroClass.toZero","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toCommRing","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","PartialOrder.toPreorder","Pi.instZero","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instCommMonoid","Real.instCommMonoidWithZero","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instPreorder","Real.instRCLike","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.pi","Set.univ","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","funext","id","instClosedIciTopology","instHasSolidNormReal","instMulZeroClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductDensity","name":"GinibrePoincare.pi_withDensity_ofReal_eq_unconditional","type_dependencies":["ENNReal.ofReal","Eq","Fin","Fin.fintype","Finset.prod","Finset.univ","LE.le","Measurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.pi","MeasureTheory.Measure.withDensity","MeasureTheory.SigmaFinite","Nat","OfNat.ofNat","Real","Real.instCommMonoid","Real.instLE","Real.instZero","Real.measurableSpace","Zero.toOfNat0"],"value_dependencies":["CommMonoid","CommSemiring.toCommMonoid","DFunLike.coe","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_prod_of_nonneg","Eq","Eq.mpr","Eq.rec","Eq.refl","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.univ","GinibrePoincare.lintegral_fin_prod_eq_prod","LE.le","Measurable","Measurable.ennreal_ofReal","MeasurableSet","MeasurableSet.univ_pi","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi_eq","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_pi_pi","MeasureTheory.Measure.withDensity","MeasureTheory.Restrict.sigmaFinite","MeasureTheory.SigmaFinite","MeasureTheory.SigmaFinite.withDensity_ofReal","MeasureTheory.lintegral","MeasureTheory.withDensity_apply","Membership.mem","Nat","OfNat.ofNat","Real","Real.instCommMonoid","Real.instLE","Real.instZero","Real.measurableSpace","Set","Set.pi","Set.univ","SetLike.instMembership","Zero.toOfNat0","congrArg","congrFun'","funext","id","instCountableFin"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarAdjointTestMap","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarCompactTestSpace","InnerProductSpace.toNormedSpace","LinearMap","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Submodule.addCommMonoid","Submodule.module","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddHom.mk","Complex","Complex.instAddCommMonoid","Complex.instNormedField","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarAdjointTestMap._proof_1","GinibrePoincare.planarAdjointTestMap._proof_2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarDbarAdjoint","InnerProductSpace.toNormedSpace","LinearMap.mk","Membership.mem","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype.val","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarAdjointTestMap._proof_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Eq","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarDbarAdjoint","HAdd.hAdd","InnerProductSpace.toNormedSpace","Membership.mem","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Real","Real.instRCLike","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.setLike","Subtype.val","instHAdd","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And.left","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.PlanarCompactTest","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ormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticBergmanComplex","name":"GinibrePoincare.planarBergmanKernelClosed._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarBergmanKernel._proof_1","GinibrePoincare.planarBergmanKernel._proof_2","GinibrePoincare.planarBergmanKernel._proof_3","GinibrePoincare.planarBergmanKernel._proof_5","GinibrePoincare.planarBergmanKernel._proof_7","GinibrePoincare.planarBergmanKernel._proof_8","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeightedAdjointTestL2","InnerProductSpace.toNormedSpace","IsClosed","LinearMap.range","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","RingHomSurjective.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.coe","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.orthogonal","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.of_le","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarBergmanKernel._proof_1","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeakDbarKernel_complex_smul_mem._proof_1","GinibrePoincare.planarWeightedAdjointTestL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap.range","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonA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","ENat.instNatCast","ENorm","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional.rclike_to_real","Function.comp","Function.hasSMul","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.entire_eq_monomial_of_unit_circle","GinibrePoincare.measurePreserving_complex_mul_of_norm_one","GinibrePoincare.mem_planarWeakDbarKernel_iff_holomorphic_representative","GinibrePoincare.planarBergmanKernel","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarLebesguePhase","GinibrePoincare.planarPotentialHalfWeight","GinibrePoincare.planarWeakDbarKernel","GinibrePoincare.planarWeakDbarKernel_has_holomorphic_representative._proof_1","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsCancelMulZero.toIsRightCancelMulZero","IsDomain.toIsCancelMulZero","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.MemLp.toLp_congr","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMonoid","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.exp_ne_zero","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.toMul","Se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inormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.instMul","Pi.instNeg","Pi.instSub","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Rat.rawCast","Real","Real.commRing","Real.contDiff_exp","Real.denselyNormedField","Real.exp","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StrongDual","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","add_apply","add_zero","congr","congrArg","congrFun'","contDiff_const","continuous_const","eq_self","fderiv","funext","id","inferInstance","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPolynormableSpace","instSMulOfMul","instZeroENat","measureSpaceOfInnerProductSpace","neg_apply","of_eq_true","rfl","smul_apply","sub_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"GinibrePoincare.planarDbar_bochner_identity","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","ContDiff","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","GinibrePoincare.planarDbarAdjointOfParts","GinibrePoincare.planarDbarOfParts","GinibrePoincare.planarLaplacian","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.exp","Real.instAdd","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddUnits","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","Bool.true","BorelSpace.opensMeasurable","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.I","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","ContDiff","ContDiff.add","ContDiff.comp","ContDiff.continuous","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiff.mul","ContDiff.neg","ContDiff.of_le","ContDiff.pow","ContDiff.sub","Continuous","Continuous.add","Continuous.clm_apply","Continuous.div_const","Continuous.integrable_of_hasCompactSupport","Continuous.mul","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.neg","ContinuousLinearMap.neg_apply","ContinuousLinearMap.smul_apply","ContinuousLinearMap.sub","ContinuousLinearMap.sub_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.metrizableSpace","ENat","ENat.instNatCast","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toAddMonoid","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.support","GinibrePoincare.integral_fderiv_complex_imag_eq_zero","GinibrePoincare.integral_fderiv_complex_real_eq_zero","GinibrePoincare.planarDbarAdjointOfParts","GinibrePoincare.planarDbarOfParts","GinibrePoincare.planarDbarOfParts._proof_1","GinibrePoincare.planarDerivative","GinibrePoincare.planarLaplacian","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.add","HasCompactSupport.fderiv_apply","HasCompactSupport.mono","HasCompactSupport.mul_left","HasCompactSupport.mul_right","HasCompactSupport.sub","HasFDerivAt","HasFDerivAt.add","HasFDerivAt.const_mul","HasFDerivAt.exp","HasFDerivAt.fderiv","HasFDerivAt.mul","HasFDerivAt.neg","HasFDerivAt.pow","HasFDerivAt.sub","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_add","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.Nor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athlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast_one","Nat.instCommSemiring","Nat.mul","Nat.rawCast","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","fderiv_const_mul","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instSMulOfMul","rfl","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceLogDistribution","name":"GinibrePoincare.planarDbar_contDiff","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.planarDbar","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.denselyNormedField","Real.instRCLike","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAdd","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","ContDiff","ContDiff.add","ContDiff.mul","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Field.toSemifield","GinibrePoincare.planarDbarOfParts._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","_private.GinibrePoincare.Analysis.CorrespondenceLogDistribution.0.GinibrePoincare.directional_contDiff","contDiff_const","fderiv","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundary","name":"GinibrePoincare.planarDbar_contDiff_infty","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.planarDbar","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.denselyNormedField","Real.instRCLike","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["Complex","Complex.I","Complex.instNormedAddCommGroup","Complex.instOne","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.finiteComplexDbar_contDiff","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","Real","Real.denselyNormedField","Real.instRCLike","Top.top","WithTop.some","instInnerProductSpaceRealComplex","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenFundamental","name":"GinibrePoincare.planarDbar_continuous","type_dependencies":["Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.planarDbar","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAdd","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","ContDiff","ContDiff.continuous_fderiv","Continuous.add","Continuous.clm_apply","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq.refl","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.planarDbarOfParts._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Nat.cast_one","Nat.cast_zero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","fderiv","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOneENat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarDbar_eq_zero_of_holomorphic","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instZero","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","GinibrePoincare.planarDbar","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.I","Complex.I_mul_I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instDenselyNormedField","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.map_smul","ContinuousLinearMap.restrictScalars","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt.fderiv_restrictScalars","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivisionRing.toRing","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.planarDbar","GinibrePoincare.planarDbarOfParts._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","Inv.inv","InvolutiveNeg.toNeg","IsScalarTower.right","LinearMap.IsScalarTower.compatibleSMul","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_neg_cancel","congr","congrArg","congrFun'","deriv","eq_self","fderiv","fderiv_eq_smul_deriv","id","instHAdd","instHDiv","instHMul","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","mul_assoc","mul_one","neg_mul","of_eq_true","one_div","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenHomotopy","name":"GinibrePoincare.planarDbar_mul","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAdd","Complex.instMul","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","GinibrePoincare.planarDbar","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.instMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHAdd","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.planarDbar","GinibrePoincare.planarDbar.eq_1","GinibrePoincare.planarDbarOfParts._proof_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv",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,"SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","hasFDerivAt_const","hasFDerivAt_id","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instPolynormableSpace","map_neg","rfl","zero_sub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductTensorMollification","name":"GinibrePoincare.planarDbar_translate","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Complex.instSub","Eq","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarDbar","HSub.hSub","Membership.mem","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.val","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","And.left","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instSub","Complex.instT2Space","Complex.instZero","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.comp_id","ContinuousLinearMap.funLike","ContinuousLinearMap.id","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","Function.comp","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexCompactTestSpace._proof_2","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarDbar","GinibrePoincare.planarDbarOfParts._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","HasFDerivAt.comp","HasFDerivAt.fderiv","HasFDerivAt.sub_const","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","Submodule","Submodule.setLike","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.natCast","WithTop.zero","Zero.toOfNat0","congrArg","fderiv","hasFDerivAt_id","id","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundary","name":"GinibrePoincare.planarDbar_tsupport_subset","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","GinibrePoincare.planarDbar","LE.le","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","UniformSpace.toTopologicalSpace","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Classical.byContradiction","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","DivInvMonoid.toInv","Eq","Eq.trans","Field.toSemifield","Function.support","GinibrePoincare.planarDbar","GinibrePoincare.planarDbarOfParts._proof_1","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instMembership","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","closure_minimal","congr","congrArg","congrFun'","eq_self","fderiv","fderiv_of_notMem_tsupport","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","isClosed_tsupport","of_eq_true","one_div","tsupport","zero_apply"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"GinibrePoincare.planarDerivative","type_dependencies":["Complex","Real"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarDerivative.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","GinibrePoincare.planarDerivative","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.planarDerivative","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarGaugeMultiplier","type_dependencies":["Complex","Real"],"value_dependencies":["Complex","Complex.instMul","Complex.ofReal","HMul.hMul","Real","Real.exp","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarGaugeMultiplier_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","C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ureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.integrable_normed","ContDiffBump.integral_normed","ContDiffBump.integral_normed_smul","ContDiffBump.nonneg_normed","ContDiffBump.normed","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually.of_forall","FiniteDimensional.rclike_to_real","Function.support","GinibrePoincare.integrable_planarL2BumpIntegrand","GinibrePoincare.planarL2BumpAverage","GinibrePoincare.planarL2BumpAverage._proof_1","GinibrePoincare.planarL2BumpAverage._proof_2","GinibrePoincare.planarL2BumpAverage._proof_3","GinibrePoincare.planarL2BumpAverage._proof_4","GinibrePoincare.planarL2Translate","GinibrePoincare.planarL2Translate._proof_1","GinibrePoincare.planarL2Translate._proof_2","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsTopologicalAddGroup.toContinuousAdd","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_const","MeasureTheory.Integrable.smul_const","MeasureTheory.IsLocallyFiniteMeasure","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.IsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_mul_const","MeasureTheory.integral_sub","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.norm_integral_le_of_norm_le","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSMulClass","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.decidableEq","Real.instAddCommMonoid","Real.instAddGroup","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","SetLike.instMembership","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Subtype","Trans.trans","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congr","congrArg","congrFun'","dite","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComple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oMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instMonoid","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","funext","id","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","map_smul","measureSpaceOfInnerProductSpace","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.planarL2BumpAverage_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CompleteSpace","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.rOut","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Tendsto","Filter.atTop","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2BumpAverage","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","nhds"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.sub","And","And.casesOn","And.right","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.normed","ContDiffBump.rOut","ContDiffBump.support_normed_eq","Continuous.continuousAt","ContinuousAt","Dist.dist","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Exists.intro","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.atTop","Filter.eventually_atTop","FiniteDimensional.rclike_to_real","Function.support","GE.ge","GT.gt","GinibrePoincare.continuous_planarL2Translate","GinibrePoincare.planarL2BumpAverage","GinibrePoincare.planarL2BumpAverage_error_le","GinibrePoincare.planarL2Translate","GinibrePoincare.planarL2Translate_zero","GroupWithZero.toDivInvMonoid","HDiv.hDiv","HSub.hSub","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans_lt","LT.lt","LT.lt.le","LT.lt.trans","Lattice.toSemilatticeSup","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","Metric.ball","Metric.continuousAt_iff","Metric.mem_ball","Metric.tendsto_atTop","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instLattice","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonAssocSemiring.toAddCommMonoidWithOne","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toL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atelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instMul","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","conj_trivial","eq_self","fact_one_le_two_ennreal","id","innerSL","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instTrivialStarReal","measureSpaceOfInnerProductSpace","mul_comm","of_eq_true","starRingEnd"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.planarL2Translate","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","FiniteDimensional.rclike_to_real","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DFunLike.coe","DomAddAct","DomAddAct.instVAddSubtypeAEEqFunMemAddAddSubgroupLp","DomAddAct.mk","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","FiniteDimensio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ocSemiring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instSeparatelyContinuousAddOfContinuousAdd","instVAddOfAdd","measurableVAdd_of_add","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.planarL2Translate.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","DFunLike.coe","DomAddAct","DomAddAct.instVAddSubtypeAEEqFunMemAddAddSubgroupLp","DomAddAct.mk","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","GinibrePoincare.planarL2Translate._proof_1","GinibrePoincare.planarL2Translate._proof_2","GinibrePoincare.planarL2Translate._proof_3","GinibrePoincare.planarL2Translate._proof_4","HVAdd.hVAdd","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHVAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instVAddOfAdd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","GinibrePoincare.planarL2Translate._proof_1","GinibrePoincare.planarL2Translate._proof_2","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.planarL2Translate_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","HSub.hSub","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddZero.toAdd","Ad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CommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.measurableSpace","ContinuousAdd.measurableAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Filter.Eventually","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional.rclike_to_real","Function.hasSMul","GinibrePoincare.planarL2Translate","GinibrePoincare.planarL2Translate_ae","HAdd.hAdd","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.IsAddLeftInvariant.isAddRightInvariant","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.eventually_add_right_iff","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","id","instHAdd","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSeparatelyContinuousAddOfContinuousAdd","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarL2Mollification","name":"GinibrePoincare.planarL2Translate_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","FiniteDimensional.rclike_to_real","GinibrePoincare.planarL2Translate","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Meas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iring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace._proof_2","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.measurableSpace","Eq","GinibrePoincare.complexMulMeasurableEquiv","GinibrePoincare.l2PullbackEquiv","GinibrePoincare.measurePreserving_complex_mul_of_norm_one","GinibrePoincare.planarLebesguePhase._proof_1","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticBergmanPhase","name":"GinibrePoincare.planarLebesguePhase._proof_1","type_dependencies":["Complex","Complex.instNorm","Complex.instZero","Eq","Ne","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","Complex","Complex.instNorm","Complex.instNormedField","Complex.instZero","Eq","Eq.mp","Eq.trans","False","False.elim","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Real","Real.instFloorRing","Real.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Zero.toOfNat0","congrArg","congrFun'","norm_zero","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralRadialProjectionPhase","name":"GinibrePoincare.planarLebesguePhase.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarLebesguePhase","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddM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ormSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_of_heq","fact_one_le_two_ennreal","fourierCoeff","funext","id","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace","not_false_eq_true","of_eq_true","one_mul","one_ne_zero._simp_1","outParam"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticProductBergman","name":"GinibrePoincare.planarLeftBergmanProjection","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.l2ProductLeftOperator","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarLeftBergmanProjection._proof_1","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.natCast","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductBergman","name":"GinibrePoincare.planarLeftBergmanProjection._proof_1","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.SigmaFinite","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup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iring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarMollifierOperator","name":"GinibrePoincare.planarMollifierLinear._proof_3","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarMollifierOperator","name":"GinibrePoincare.planarMollifierLinear._proof_4","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarMollifierOperator","name":"GinibrePoincare.planarMollifierLinear._proof_5","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarMollifierOperator","name":"GinibrePoincare.planarMollifierLinear._proof_6","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPlanarMollifierOperator","name":"GinibrePoincare.planarMollifierLinear._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","FiniteDimensional.rclike_to_real","GinibrePoincare.planarMollifierLinear._proof_3","GinibrePoincare.planarMollifierLinear._proof_6","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instNormedAddCom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is.NonQuadraticPiBergman","name":"GinibrePoincare.planarPiBergmanCoordinate.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.l2PiCoordinateOperator","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarPiBergmanCoordinate","GinibrePoincare.planarPiBergmanCoordinate._proof_1","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq.refl","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.planarPiBergmanCoordinate","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetri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uousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","Fin","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.l2PiCoordinateOperator_idempotent","GinibrePoincare.planarBergmanKernelClosed","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPiBergmanCoordinate._proof_1","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.isIdempotentElem_starProjection","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiBergman","name":"GinibrePoincare.planarPiBergmanCoordinate_norm_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.planarPiBergmanCoordinate","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instLE","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.l2PiCoordinateOperator","GinibrePoincare.l2PiCoordinateOperator_norm_le","GinibrePoincare.planarBergmanKernelClosed","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPiBergmanCoordinate._proof_1","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le.trans","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAs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CommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.ndrec","Eq.refl","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.l2PiCoordinateOperators_commute","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarPiBergmanCoordinate","GinibrePoincare.planarPiBergmanCoordinate._proof_1","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","dite","fact_one_le_two_ennreal","instAddNat","instDecidableEqFin","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPiBergmanMonomials","name":"GinibrePoincare.planarPiBergmanJointKernel","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measu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roup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.id","ContinuousLinearMap.isClosed_ker","ContinuousLinearMap.sub","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.planarPiBergmanJointKernel","GinibrePoincare.planarPiBergmanJointKernel._proof_1","GinibrePoincare.planarPiBergmanJointKernel._proof_3","GinibrePoincare.planarPiBergmanJointKernel._proof_4","GinibrePoincare.planarPiBergmanJointKernel._proof_5","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.planarPiBergmanProjection_mem_weighted_monomial_closure","GinibrePoincare.planarPiWeightedMonomialVector_fixed","GinibrePoincare.planarPiWeightedMonomialVectors","GinibrePoincare.planarPiWeightedMonomialVectors._proof_1","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","SetLike.coe","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.instPartialOrder","Submodule.setLike","Submodule.span","Submodule.span_le","Submodule.topologicalClosure","Submodule.topologicalClosure_minimal","SubtractionMonoid.toSubNegZeroMonoid","Subtype","T5Space.toT1Space","T6Space.toT5Space","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instAddNat","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instT6SpaceOfMetrizableSpace","le_antisymm","measureSpaceOfInnerProductSpace","sub_eq_zero","sub_self"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPiBergman","name":"GinibrePoincare.planarPiBergmanProjection","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","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orelSpace","Complex.instCompleteSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.adjoint","ContinuousLinearMap.comp","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.ndrec","EquivLike.toFunLike","Exists","Exists.casesOn","Field.toCommRing","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.complexSuccessiveProjections_adjoint","GinibrePoincare.planarPiBergmanCoordinate","GinibrePoincare.planarPiBergmanCoordinate_adjoint","GinibrePoincare.planarPiBergmanCoordinates_commute","GinibrePoincare.planarPiBergmanProjection._proof_1","HAdd.hAdd","Iff.mp","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","List","List.finRange","List.instMembership","List.map","List.mem_map","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","smulCommClass_self","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPartitionVandermonde","name":"GinibrePoincare.planarPiBergmanProjection_commutes_alternation","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.volumeAlternationOperator","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRi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rePoincare.planarPiBergmanProjection_pure","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.SigmaFinite","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.isIdempotentElem_starProjection","Submodule.starProjection","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","congr","congrArg","fact_one_le_two_ennreal","funext","id","instAddNat","instHAdd","instHMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiBergmanMonomials","name":"GinibrePoincare.planarPiBergmanProjection_mem_weighted_monomial_closure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.planarPiWeightedMonomialVectors","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.span","Submodule.topologicalClosure","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","ClosedSubmodule.toSubmodule","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.zero","ContinuousMultilinearMap","ContinuousMultilinearMap.funLike","DFunLike.coe","DFunLike.congr_fun","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Exists.intro","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.continuousMultilinear_mem_of_closed_factor_spans","GinibrePoincare.l2PiOperators_ext_on_pure","GinibrePoincare.l2PiProductContinuousMultilinear","GinibrePoincare.l2PiProductVector","GinibrePoincare.planarBergmanKernelClosed","GinibrePoincare.planarBergmanKernel_le_weighted_monomial_closure","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.planarPiBergmanProjection_pure","GinibrePoincare.planarPiWeightedMonomialVectors","GinibrePoincare.planarPiWeightedMonomialVectors._proof_1","GinibrePoincare.planarPiWeightedMonomialVectors._proof_2","GinibrePoincare.planarPiWeightedMonomialVectors._proof_3","GinibrePoincare.planarWeightedMonomialVectors","HAdd.hAdd","HMul.hMul","HasQuotient.Quotient","Iff.mp","Iff.mpr","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsClosed","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","Nat","Nat.instAtLeastT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Poincare.planarPiWeightedMonomialVectors","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","LinearMap.range","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instOne","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomSurjective.ids","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.instPartialOrder","Submodule.setLike","Submodule.span","Submodule.topologicalClosure","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instAddNat","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","le_antisymm","measureSpaceOfInnerProductSpace","sub_eq_zero","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingMonomialClosure","name":"GinibrePoincare.planarPiBergman_alternating_mem_alternated_monomial_closure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.configurationVolume","GinibrePoincare.permutationSign","GinibrePoincare.planarPiAlternatedWeightedMonomialVectors","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.volumePermutationL2","HAdd.hAdd","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","Measu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Ring","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomSurjective.ids","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.coe","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.t2Space_of_metrizableSpace","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","closure","congrArg","congrFun'","continuous_const","eq_self","fact_one_le_two_ennreal","funext","id","instAddNat","instHAdd","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","isClosed_eq","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","of_eq_true","secondCountable_of_proper","smul_zero","sub_apply","sub_eq_zero"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPiCompactGraphApproximation","name":"GinibrePoincare.planarPiCompactGraphAverage","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","ContDiffBump","Continuous","GinibrePoincare.Configuration","GinibrePoincare.PlanarPiDbarGraphSpace","HAdd.hAdd","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","Continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarPiCompactGraphAverage._proof_1","GinibrePoincare.planarPiCompactGraphAverage._proof_3","GinibrePoincare.planarPiCompactGraphAverage._proof_4","GinibrePoincare.planarPiNormalizedBumpTest","GinibrePoincare.planarPiPureDbarGraph","HAdd.hAdd","HSMul.hSMul","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","Prod.instSMul","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCo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inormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","And.intro","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofRealCLM","Complex.ofReal_zero","ContDiff","ContDiff.comp","ContDiffBump","ContDiffBump.contDiff_normed","ContDiffBump.hasCompactSupport_normed","ContDiffBump.normed","ContDiffBump.toFun","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Div.div","DivInvMonoid.toDiv","ENat","ENat.instNatCast","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","GinibrePoincare.planarComplexCompactTestSpace._proof_2","HasCompactSupport","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Nat.cast","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiWeightedMollification","name":"GinibrePoincare.planarPiNormalizedBumpTest.eq_1","type_dependencies":["Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.normed","Eq","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarPiNormalizedBumpTest","GinibrePoincare.planarPiNormalizedBumpTest._proof_1","GinibrePoincare.planarPiNormalizedBumpTest._proof_2","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Real","Real.instRCLike","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.mk","Zero.toOfNat0","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.instZero","ContDiffBump","Eq.refl","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.planarPiNormalizedBumpTest","OfNat.ofNat","Zero.toOfNat0"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticPiDbarClosure","name":"GinibrePoincare.planarPiPureDbarGraph","type_dependencies":["Complex","Complex.instNormedField","Continuous","Fin","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace","HAdd.hAdd","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Continuous","Fin","Fin.fintype","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.planarPiPureWeightedDbar","GinibrePoincare.planarPiPureWeightedValue","HAdd.hAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.ins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","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Filter.Eventually","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.prod_mul_distrib","Finset.univ","Function.eval","Function.update","Function.update_congr","Function.update_of_ne","Function.update_self","GinibrePoincare.Configuration","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.l2PiProductVector","GinibrePoincare.l2PiProductVector_coeFn","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.piSeparatedDbarKernel","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexCompactTestSpace._proof_2","GinibrePoincare.planarComplexCompactTest_dbar_compact","GinibrePoincare.planarComplexCompactTest_dbar_continuous","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarComplexTestTranslate_weightedDbar","GinibrePoincare.planarComplexWeightedDbarL2","GinibrePoincare.planarComplexWeightedValueL2","GinibrePoincare.planarDbar","GinibrePoincare.planarPiPureWeightedDbar","GinibrePoincare.planarPotentialHalfWeight","GinibrePoincare.planarWeightedTranslateFunction","GinibrePoincare.planarWeightedTranslateL2","GinibrePoincare.planarWeightedTranslate_memLp","HAdd.hAdd","HMul.hMul","HSub.hSub","HasCompactSupport","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.Measure.quasiMeasurePreserving_eval","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.ae","MeasureTheory.ae_all_iff","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.property","Subtype.val","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","congr","congrArg","congrFun","congrFun'","dite","funext","id","instAddNat","instCountableFin","instDecidableEqFin","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiTensorMollification","name":"GinibrePoincare.planarPiTranslatedGraph_continuous","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Fin.fintype","GinibrePoincare.Pl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inibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.finiteDimensionalL2_kernel_integral_ae","GinibrePoincare.finiteTranslatedKernel_hasCompactSupport","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.piPotentialHalfWeight_continuous","GinibrePoincare.piSeparatedDbarKernel","GinibrePoincare.piSeparatedDbarKernel_compact","GinibrePoincare.piSeparatedDbarKernel_continuous","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarPiPureDbarGraph","GinibrePoincare.planarPiPureWeightedDbar","GinibrePoincare.planarPiTranslatedDbar_coeFn","GinibrePoincare.planarPiTranslatedGraph_integrable","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.mul_right","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.isLocallyFiniteMeasure","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_mul_const","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.addGroup","Pi.borelSpace","Pi.complete","Pi.instMul","Pi.instSub","Pi.isTopologicalAddGroup","Pi.module","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.instSMul","Prod.mk","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Subtype","Subtype.val","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","congrArg","continuous_fst","continuous_snd","fact_one_le_two_ennreal","id","instAddNat","instCountableFin","instHAdd"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cPiTensorConvolution","name":"GinibrePoincare.planarPiTranslatedGraph_integral_value_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.commRing","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.measurableSpace","Continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.EventuallyEq","Fin","Fin.fintype","Finset.prod","Finset.univ","Function.hasSMul","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarPiPureDbarGraph","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod.fst","Prod.instSMul","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instAddNat","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","And.left","And.right","CommRing.toCommMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.commRing","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","Continuous","Continuous.comp","Continuous.mul","Continuous.sub","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toDivisionRing","Filter.Eventually.mono","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finite.of_fintype","FiniteDimensional.finiteDimensional_pi'","Finset","Finset.instSetLike","Finset.prod","Finset.univ","Function.comp","Function.hasSMul","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.finiteDimensionalL2_kernel_integral_ae","GinibrePoincare.finiteTranslatedKernel_hasCompactSupport","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.piPotentialHalfWeight_continuous","GinibrePoincare.piSeparatedKernel_hasCompactSupport","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexCompactTestSpace._proof_2","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarPiPureDbarGraph","GinibrePoincare.planarPiPureWeightedValue","GinibrePoincare.planarPiTranslatedGraph_integrable","GinibrePoincare.planarPiTranslatedValue_coeFn","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.mul_right","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Integrable","MeasureTheory.Integrable.fst","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.Measure.pi.isLocallyFiniteMeasure","MeasureTheory.Measure.pi.sigmaFinite","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_mul_const","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.addGroup","Pi.borelSpace","Pi.complete","Pi.instMul","Pi.instSub","Pi.isTopologicalAddGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","Prod","Prod.fst","Prod.instSMul","Prod.mk","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMe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incare.planarPiWeightedMonomialVectors._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiBergmanMonomials","name":"GinibrePoincare.planarPiWeightedMonomialVectors._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiBergmanMonomials","name":"GinibrePoincare.planarPiWeightedMonomialVectors._proof_3","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","MeasureTheory.MeasureSpace.volume","MeasureTheory.SigmaFinite","Nat","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","Fin","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarPotentialGaugeTest","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","GinibrePoincare.PlanarCompactTest","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.natCast","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarGaugeMultiplier","GinibrePoincare.planarPotentialGaugeTest._proof_1","GinibrePoincare.planarPotentialGaugeTest._proof_2","HMul.hMul","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.mk","Subtype.val","WithTop","WithTop.natCast","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarPotentialGaugeTest._proof_1","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"GinibrePoincare.planarPotentialGaugeTest._proof_2","type_dependencies":["And","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","ContDiff","DenselyNormedField.to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at","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Rat.rawCast","Real","Real.commRing","Real.continuous_exp","Real.exp","Real.exp_add","Real.instAdd","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.linearOrder","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","autoParam","congrArg","congrFun'","continuous_const","eq_of_heq","funext","heq_of_eq","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarProductCompactGraphAverage","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","ContDiffBump","Continuous","GinibrePoincare.PlanarProductDbarGraphSpace","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","Continuous","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarProductCompactTensor","GinibrePoincare.PlanarProductDbarGraphSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarNormalizedBumpTest","GinibrePoincare.planarProductCompactGraphAverage._proof_1","GinibrePoincare.planarProductCompactGraphAverage._proof_3","GinibrePoincare.planarProductCompactGraphAverage._proof_4","GinibrePoincare.planarProductCompactGraphAverage._proof_6","GinibrePoincare.planarProductDbarGraphMap","HSMul.hSMul","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Norme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ceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarProductCompactGraphAverage._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","RCLike.innerProductSpace","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarProductCompactGraphAverage._proof_5","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarProductCompactGraphAverage._proof_6","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","GinibrePoincare.planarProductCompactGraphAverage._proof_5","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"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oMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","TensorProduct.addCommMonoid","TensorProduct.instModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductDbarClosure","name":"GinibrePoincare.planarProductDbarGraphMap._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductDbarClosure","name":"GinibrePoincare.planarProductDbarGraphMap._proof_2","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductDbarClosure","name":"GinibrePoincare.planarProductDbarGraphMap._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","GinibrePoincare.planarProductDbarGraphMap._proof_2","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceO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UnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instZero","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","secondCountable_of_proper"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.rOut","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.symm","Eq.trans","Field.toDivisionRing","Filter.Tendsto","Filter.atTop","FiniteDimensional.rclike_to_real","GinibrePoincare.planarMollifierOperator","GinibrePoincare.planarMollifierOperator_norm_le","GinibrePoincare.planarMollifierOperator_tendsto","GinibrePoincare.productL2_left_strong_limit","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NNNorm.nnnorm","NNReal","NNReal.instOne","NNReal.instPartialOrder","NNReal.instSemiring","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instLE","Real.instNatCast","Real.instOne","Real.instRing","Real.instZero","Real.pseudoMetricSpace","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCo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ibrePoincare.Analysis.NonQuadraticProductDbar.0.GinibrePoincare.planarProductLeft_inverse_action._abel_1_10","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instAddTensorProduct","instHAdd","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroTensorProduct","locallyCompact_of_proper","map_add","map_sub","map_zero","measureSpaceOfInnerProductSpace","of_eq_true","secondCountable_of_proper","sub_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductMollifierLimit","name":"GinibrePoincare.planarProductMollifier_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.rOut","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.Tendsto","Filter.atTop","FiniteDimensional.rclike_to_real","GinibrePoincare.l2ProductLeftOperator","GinibrePoincare.l2ProductRightOperator","GinibrePoincare.planarMollifierOperator","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instZero","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","secondCountable_of_proper"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.rOut","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.Tendsto","Filter.atTop","FiniteDimensional.rclike_to_real","GinibrePoincare.contractions_strong_limit_apply","GinibrePoincare.l2ProductLeftOperator","GinibrePoincare.l2ProductLeftOperator_norm_le","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HaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsFiniteMeasureOnCompacts","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","Membership.mem","Module.toDistribMulAction","Module.toMulActionWithZero","MulActionWithZero.toSMulWithZero","Nat","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.smul'","PolynormableSpace.continuousSMul","Prod","Prod.continuousSMul","Prod.fst","Prod.instAddCommMonoid","Prod.instMeasurableSpace","Prod.instModule","Prod.instSMul","Prod.normedAddCommGroup","Prod.opensMeasurableSpace","Prod.smulWithZero","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule.addCommMonoid","Submodule.module","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TensorProduct.addCommMonoid","TensorProduct.instModule","TensorProduct.tmul","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instOfNatAtLeastTwo","instPolynormableSpace","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductTensorMollification","name":"GinibrePoincare.planarProductTranslatedTensorGraph_integral_mem","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Continuous","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarProductCompactTensor","GinibrePoincare.PlanarProductDbarGraphSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarProductDbarClosedGraph","GinibrePoincare.planarProductDbarGraphMap","HSMul.hSMul","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDi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roup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Field.toDivisionRing","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarProductCompactTensor","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarProductWeightedDbarRight","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","TensorProduct.addCommMonoid","TensorProduct.instModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.rec","Eq.refl","Field.toDivisionRing","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarProductCompactTensor","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarProductWeightedDbarRight","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.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emiring","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarShrinkingBump._proof_3","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarShrinkingBump._proof_4","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Field.toSemifield","GinibrePoincare.planarShrinkingBump._proof_3","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","LT.lt","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instAdd","Real.instDivInvMonoid","Real.instField","Real.instNatCast","Real.instOne","Real.partialOrder","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","instHAdd","instHDiv","instOfNatAtLeastTwo"],"value_dependencies":["DivInvMonoid.toDiv","Field.toSemifield","GinibrePoincare.planarShrinkingBump._proof_2","HAdd.hAdd","HDiv.hDiv","IsStrictOrderedRing.toPosMulStrictMono","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Real","Real.instAdd","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instNatCast","Real.instOne","Real.linearOrder","Real.partialOrder","Real.semiring","half_lt_self","instHAdd","instHDiv","instMulZeroClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.planarShrinkingBump_rOut_tendsto","type_dependencies":["Complex","Complex.instZero","ContDiffBump.rOut","Filter.Tendsto","Filter.atTop","GinibrePoincare.planarShrinkingBump","Nat","Nat.instPreorder","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.toModule","CommSemiring.toSemiring","DistribMulAction.toMulAction","DivisionRing.toRing","DivisionSemiring.toNNRatAlgebra","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","IsScalarTower.nnrat","Module.toDistribMulAction","NNRat","NNRat.instContinuousSMulOfIsScalarTowerOfRat","NNRat.instContinuousSMulRatReal","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Rat","Rat.instCharZero","Rat.instField","Rat.instNormedField","Rat.monoid","Rat.semiring","Real","Real.instAddCommMonoid","Real.instField","Real.instFloorRing","Real.instRCLike","Real.instRing","Real.linearOrder","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","UniformSpace.toTopologicalSpace","instCommSemiringNNRat","normedAlgebraRat","tendsto_one_div_add_atTop_nhds_zero_nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarTestLpLift","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheo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ibrePoincare.planarDbarAdjoint","GinibrePoincare.planarUngaugedL2Function","GinibrePoincare.planarWeakDbarKernel","GinibrePoincare.planarWeakDbarKernel_unweighted_test_equation._proof_1","HMul.hMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submodule","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","Complex.re","ContDiff","ContDiff.of_le","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.mem_planarWeakDbarKernel_iff","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbarAdjoint","GinibrePoincare.planarPotentialGaugeTest","GinibrePoincare.planarUngaugedL2Function","GinibrePoincare.planarWeakDbarKernel","GinibrePoincare.planarWeakDbarKernel_unweighted_test_equation._proof_1","GinibrePoincare.planarWeightedAdjointTestL2","HMul.hMul","Iff.mp","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRi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","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.instNormedField","Continuous","GinibrePoincare.planarTestLpLift","GinibrePoincare.planarWeightedTestMap","GinibrePoincare.planarWeightedTestMap_memLp","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarWeightedTestL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeightedTestL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","Eq.rec","Eq.refl","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeightedTestL2","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.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oid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.integral_norm_sq_eq_L2_norm_sq","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeightedTestL2","GinibrePoincare.planarWeightedTestMap","GinibrePoincare.planarWeightedTestMap_memLp","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_half_weight_norm","congrArg","id","instHMul","instHPow","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.planarWeightedTestL2_weak_derivative","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.continuous","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Field.toDivisionRing","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeightedAdjointTestL2","GinibrePoincare.planarWeightedDbarTestL2","GinibrePoincare.planarWeightedTestL2","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalS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","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticBergmanRadial","name":"GinibrePoincare.planarWeighted_radial_zeroMean_orthogonal_kernel","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.im","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Complex.ofReal","Complex.re","ContDiff","ContDiff.continuous","ContDiff.of_le","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeakDbarKernel","GinibrePoincare.planarWeightedTestL2","GinibrePoincare.planarWeighted_radial_zeroMean_orthogonal_kernel._proof_1","HMul.hMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.exp","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.orthogonal","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","And","And.casesOn","And.left","And.right","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.continuous_re","Complex.im","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","Complex.reCLM","Complex.zero_re","ContDiff","ContDiff.continuous","ContDiff.of_le","Continuous","Continuous.comp","Continuous.integrable_of_hasCompactSupport","Continuous.mul","Continuous.smul","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.integral_comp_comm","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Differentiable","Differentiable.continuous","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.mem_planarWeakDbarKernel_iff_holomorphic_representative","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPotentialHalfWeight","GinibrePoincare.planarWeakDbarKernel","GinibrePoincare.planarWeakDbarKernel_has_holomorphic_representative._proof_1","GinibrePoincare.planarWeightedTestL2","GinibrePoincare.planarWeightedTestMap","GinibrePoincare.planarWeightedTestMap_memLp","GinibrePoincare.planarWeighted_radial_zeroMean_orthogonal_kernel._proof_1","GinibrePoincare.radialPotential_compact_holomorphic_pairing","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.mul_right","HasCompactSupport.smul_right","Iff.mp","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LinearMap","LinearMap.instFunLike","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isInt","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul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","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","not_false_eq_true","of_eq_true","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarAdjoint","name":"GinibrePoincare.planar_weighted_derivative_ibp","type_dependencies":["Complex","Complex.I","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","GinibrePoincare.planarDerivative","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Neg.neg","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Or","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.exp","Real.instMul","Real.instNeg","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instHMul","instHSub","instInnerProductSpaceRealComplex","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.false","BorelSpace.opensMeasurable","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.measurableSpace","ContDiff","ContDiff.comp","ContDiff.continuous","ContDiff.continuous_fderiv","ContDiff.differentiable","ContDiff.mul","ContDiff.neg","Continuous","Continuous.clm_apply","Continuous.integrable_of_hasCompactSupport","Continuous.mul","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsNegApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.neg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","EMetricSpace.metrizableSpace","ENat","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.integral_fderiv_complex_imag_eq_zero","GinibrePoincare.integral_fderiv_complex_real_eq_zero","GinibrePoincare.planarDerivative","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasCompactSupport","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","HasCompactSupport.mul_right","HasFDerivAt","HasFDerivAt.exp","HasFDerivAt.fderiv","HasFDerivAt.mul","HasFDerivAt.neg","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","IsTopologicalSemiring.toIsModuleTopology","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt"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NatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorKernel","name":"GinibrePoincare.polynomialConstantIndex.eq_1","type_dependencies":["Eq","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.mk","GinibrePoincare.polynomialConstantIndex","Nat","OfNat.ofNat","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialConstantIndex","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.polynomialEigenfunction","type_dependencies":["Complex","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","Nat"],"value_dependencies":["Complex","Complex.instMul","Complex.ofReal","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.Laguerre.polynomial","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.R_poly","GinibrePoincare.S_observable","GinibrePoincare.polynomialEigenfunction._proof_1","GinibrePoincare.recenteredGammaShape","HMul.hMul","Nat","OfNat.ofNat","Polynomial.eval","Real","Real.semiring","instHMul","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.polynomialEigenfunction._proof_1","type_dependencies":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","LT.lt","Nat","Nat.decLt","OfNat.ofNat","id","instLTNat","instOfNatNat","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctions","name":"GinibrePoincare.polynomialEigenfunction.eq_1","type_dependencies":["Complex","Complex.instMul","Complex.ofReal","Eq","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.Configuration","GinibrePoincare.Laguerre.polynomial","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.R_poly","GinibrePoincare.S_observable","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunction._proof_1","GinibrePoincare.recenteredGammaShape","HMul.hMul","Nat","OfNat.ofNat","Polynomial.eval","Real","Real.semiring","instHMul","instOfNatNat"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunction","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialEigenfunctionBasis","name":"GinibrePoincare.polynomialEigenfunctionBasis","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.sumRadiusPolynomialSpace","LE.le","Membership.mem","Module.Basis","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","instLENat","instOfNatNat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunctionSpan_eq","GinibrePoincare.polynomialEigenfunction_linearIndependent","GinibrePoincare.sumRadiusPolynomialSpace","LE.le","LinearEquiv.ofEq","Membership.mem","Module.Basis.map","Module.Basis.span","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","Set.range","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.span","Subtype","instLENat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialEigenfunctionBasis.congr_simp","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Eq","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.sumRadiusPolynomialSpace","LE.le","Membership.mem","Module.Basis","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","instLENat","instOfNatNat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.sumRadiusPolynomialSpace","LE.le","Membership.mem","Module.Basis","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommM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o","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.eval","MvPolynomial.eval_rename","MvPolynomial.eval\u2082Hom","MvPolynomial.eval\u2082Hom_X'","MvPolynomial.eval\u2082_C","MvPolynomial.rename","Nat","Nat.decLt","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.le_of_lt","Nat.le_refl","Nat.succ","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalRingHomClass.toMulHomClass","OfNat.ofNat","Polynomial","Polynomial.eval","Polynomial.eval\u2082","Polynomial.eval\u2082_hom","Polynomial.hom_eval\u2082","Real","Real.semiring","RingHom","RingHom.comp","RingHom.ext","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toNonUnitalRingHomClass","Semiring.toNonAssocSemiring","SetLike.instMembership","True","congrArg","congrFun'","eq_of_heq","eq_self","funext","id","instAddNat","instHAdd","instHMul","instLTNat","instOfNatNat","map_mul","noConfusion_of_Nat","of_decide_eq_true","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctionBasis","name":"GinibrePoincare.polynomialEigenfunction_linearIndependent","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.polynomialEigenfunction","LE.le","LinearIndependent","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","instLENat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Fin","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_apply","Finset.sum_congr","Finset.sum_eq_single_of_mem","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.casesOn","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.PolynomialEigenfunctionData.mk","GinibrePoincare.ginibreMeasure","GinibrePoincare.integrable_polynomialEigenfunction_inner","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunction_equilibrium_orthogonal","GinibrePoincare.polynomialEigenfunction_inner_self_ne_zero","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mp","InnerProductSpace.toNormedSpace","LE.le","LinearIndependent","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.const_mul","MeasureTheory.integral","MeasureTheory.integral_const_mul","MeasureTheory.integral_finsetSum","MeasureTheory.integral_zero'","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Ne","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","Or","Or.resolve_right","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SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorClosure","name":"GinibrePoincare.polynomialGeneratorGraph._proof_2","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorClosure","name":"GinibrePoincare.polynomialGeneratorGraph._proof_3","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorClosure","name":"GinibrePoincare.polynomialGeneratorGraph._proof_4","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialGeneratorGraph._proof_1","GinibrePoincare.polynomialGeneratorGraph._proof_3","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorClosure","name":"GinibrePoincare.polynomialGeneratorGraph._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminorm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DivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Set.range","SetLike.instMembership","Submodule.le_topologicalClosure","Submodule.span","Submodule.subset_span","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorEigenvector.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialEigenfunctionL2","GinibrePoincare.polynomialSectorEigenvector","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorEigenvector._proof_8","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","UniformSpace.toTopologicalSpace","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAd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onAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.zero","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.inner_polynomialEigenfunctionL2","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunctionL2","GinibrePoincare.polynomialEigenfunction_inner_self_ne_zero","GinibrePoincare.polynomialSectorEigenvector","HMul.hMul","HPow.hPow","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.ofReal","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.instZero","Ring.toSemiring","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.zero","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","inner_self_eq_norm_sq_to_K","instHMul","instHPow","instInnerProductSpaceRealComplex","instLENat","instOfNatAtLeastTwo","instOfNatNat","norm_zero","not_false_eq_true","not_true_eq_false","of_eq_true","starRingEnd","zero_pow"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorEvolution","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Finsupp","Finsupp.instAddCommGroup","Finsupp.module","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorCombination","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorEvolution._proof_3","GinibrePoincare.polynomialSectorFiniteEvolution","GinibrePoincare.polynomialSector_completeSpace","LE.le","LinearMap.extendOfNorm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.toReal","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorEvolution._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Distri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iring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorEvolution_add","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.comp","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorEvolution","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","NNReal.instSemiring","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instDistribOfSemiring","instHAdd","instLENat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.exp","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_exp","Complex.ofReal_mul","Complex.ofReal_neg","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.continuous","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenseRange.induction_on","Distrib.leftDistribClass","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Fin","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instFunLike","Finsupp.linearCombination","Finsupp.module","Finsupp.support","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynom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omialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorCombination","GinibrePoincare.polynomialSectorCombination_dense","GinibrePoincare.polynomialSectorEvolution","GinibrePoincare.polynomialSectorFiniteEvolution","GinibrePoincare.polynomialSectorFiniteEvolution_contracts","GinibrePoincare.polynomialSector_completeSpace","HMul.hMul","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","LinearMap.extendOfNorm","LinearMap.instFunLike","LinearMap.norm_extendOfNorm_apply_le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Monoid.toMulAction","MulZeroOneClass.toMulOneClass","NNReal","NNReal.coe_nonneg","NNReal.toReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instLE","Real.instMul","Real.instOne","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.normedAddCommGroup","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHMul","instLENat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorEvolution_dist_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Dist.dist","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorEvolution","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.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Poincare.ginibreMeasure","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasurableSpace.pi","MeasureTheory.Lp.instIsScalarTower","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","RCLike.innerProductSpace","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","instOfNatAtLeastTwo","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSemigroup","name":"GinibrePoincare.polynomialSectorFiniteEvolution.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.linearCombination","Finsupp.module","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorEigenvector","GinibrePoincare.polynomialSectorEigenvector._proof_1","GinibrePoincare.polynomialSectorEigenvector._proof_2","GinibrePoincare.polynomialSectorEigenvector._proof_4","GinibrePoincare.polynomialSectorEigenvector._proof_5","GinibrePoincare.polynomialSectorFiniteEvolution","GinibrePoincare.polynomialSectorFiniteEvolution._proof_1","GinibrePoincare.polynomialSectorFiniteEvolution._proof_4","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.exp","Real.instMul","Real.instNeg","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","instHMul","instHSMul","instLENat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Field.toDivisionRing","Fin","Finsupp","Fin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oidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorSpectralGraph","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasSum","ContinuousLinearMap.prodMap","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","EquivLike.toFunLike","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Fin","Finset","Finset.instSetLike","Finset.sum","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.closedPolynomialGenerator_isClosed","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorHilbertBasis","GinibrePoincare.polynomialSectorSpectralGraph","HMul.hMul","HSMul.hSMul","HasSum","HasSum.prodMk","HilbertBasis","HilbertBasis.hasSum_repr","HilbertBasis.instFunLike","HilbertBasis.repr","HilbertBasis.repr_apply_apply","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsClosed.mem_of_tendsto","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearPMap.IsClosed","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoi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","Submodule.span","Submodule.span_le","Submodule.topologicalClosure","Submodule.topologicalClosure_mono","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.pseudoMetricSpace","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instHSMul","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","instUniformSpaceSubtype","propext","top_unique"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorSelfAdjoint","name":"GinibrePoincare.polynomialSectorGenerator_eigenpair","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorGenerator","GinibrePoincare.polynomialSectorHilbertBasis","HSMul.hSMul","HilbertBasis","HilbertBasis.instFunLike","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.setLike","Submodule.smul","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instLENat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Classical.propDecidable","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Comple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ureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","NNRat","Nat","Neg.neg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toLinearMapClassNNRat","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.adjoint","Submodule.ext","Submodule.innerProductSpace","Submodule.mem_adjoint_iff","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.smul","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","id","inner_smul_left","instCommSemiringNNRat","instDistribOfSemiring","instHMul","instHSMul","instHSub","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","map_neg","propext","starRingEnd","sub_eq_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorGenerator_graph_iff_ambient","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorGenerator","Iff","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialGenerator","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorGenerator","GinibrePoincare.polynomialSectorGenerator_ambient_graph_of_spectral","GinibrePoincare.polynomialSectorGenerator_graph","GinibrePoincare.polynomialSectorGenerator_spectral_of_ambient_graph","GinibrePoincare.polynomialSectorSpectralGraph","Iff","Iff.intro","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","id","instLENat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorInfinitesimalGenerator","name":"GinibrePoincare.polynomialSectorGenerator_graph_iff_right_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.closedPolynomialSector","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorGenerator","GinibrePoincare.polynomialSectorOrbit","HasDerivWithinAt","Iff","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearPMap.graph","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule"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r","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Neg.neg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","forall_congr","funext","implies_true","inner_zero_right","instHMul","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","neg_mul","neg_zero","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorSpectralGraph._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.closedPolynomialSector","GinibrePoincare.eigenvalue","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorHilbertBasis","HMul.hMul","HSMul.hSMul","HilbertBasis","HilbertBasis.instFunLike","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivis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","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommMonoid","Submodule.innerProductSpace","Submodule.module","Submodule.normedAddCommGroup","Submodule.seminormedAddCommGroup","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","inferInstance","inner_smul_right","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorSpectralGraph._proof_4","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorSpectralGraph._proof_5","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Field.toDivisionRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toSeminormedAddCommGroup","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorSpectralGraph._proof_6","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"GinibrePoincare.polynomialSectorSpectralGraph._proof_7","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass","Complex","Complex.addGroupWithOne","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialSectorSpectralGraph._proof_4","GinibrePoincare.polynomialSectorSpectralGraph._proof_6","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","Nat","Norm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up","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Ne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.instTop","Submodule.orthogonal","Submodule.setLike","Subtype","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instLENat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialSpectralEvolution","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","GinibrePoincare.Configuration","GinibrePoincare.sumRadiusPolynomialSpace","LE.le","LinearMap","Membership.mem","Nat","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Real","RingHom.id","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","instLENat","instOfNatNat"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instSemiring","Complex.ofReal","DFinsupp.instEquivLikeLinearEquiv","DFunLike.coe","EquivLike.toFunLike","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.polynomialSpectralEvolution._proof_1","GinibrePoincare.polynomialSpectralEvolution._proof_2","GinibrePoincare.sumRadiusPolynomialSpace","HMul.hMul","HSMul.hSMul","LE.le","LinearEquiv","LinearMap","LinearMap.addCommMonoid","LinearMap.module","Membership.mem","Module.Basis","Module.Basis.constr","Module.Basis.instFunLike","Nat","Neg.neg","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Real","Real.exp","Real.instMul","Real.instNeg","RingHom.id","RingHomInvPair.ids","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.smul","Subtype","instHMul","instHSMul","instLENat","instOfNatNat","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialSpectralEvolution._proof_1","type_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instSemiring","DistribMulAction.toMulAction","GinibrePoincare.Configuration","GinibrePoincare.sumRadiusPolynomialSpace","Membership.mem","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Pi.Function.module","Pi.addCommMonoid","SMulCommClass","SemigroupAction.toSMul","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype"],"value_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instAddCommMonoid","Complex.instSemiring","DistribMulAction.toMulAction","GinibrePoincare.Configuration","GinibrePoincare.sumRadiusPolynomialSpace","Membership.mem","Module.toDistribMulAction","Nat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialSpectralEvolution._proof_2","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instSemiring","DistribMulAction.toMulAction","GinibrePoincare.Configuration","IsScalarTower","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Pi.instSMul","SemigroupAction.toSMul","Semiring.toModule","Semiring.toMonoid","instSMulOfMul"],"value_dependencies":["AddC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.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialSpectralEvolution_basis","type_dependencies":["AddCommMonoid.toAddMonoid","Algebra.id","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instSemiring","Complex.ofReal","DFunLike.coe","DistribMulAction.toMulAction","Eq","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.polynomialSpectralEvolution","GinibrePoincare.sumRadiusPolynomialSpace","HMul.hMul","HSMul.hSMul","IsScalarTower.right","LE.le","LinearMap","LinearMap.instFunLike","Membership.mem","Module.Basis","Module.Basis.instFunLike","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Neg.neg","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.isScalarTower","Real","Real.exp","Real.instMul","Real.instNeg","RingHom.id","SemigroupAction.toSMul","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.smul","Subtype","instHMul","instHSMul","instLENat","instOfNatNat","instSMulOfMul"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instSemiring","Complex.ofReal","DFunLike.coe","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.polynomialSpectralEvolution._proof_1","GinibrePoincare.polynomialSpectralEvolution._proof_2","GinibrePoincare.sumRadiusPolynomialSpace","HMul.hMul","HSMul.hSMul","LE.le","Membership.mem","Module.Basis","Module.Basis.constr_basis","Module.Basis.instFunLike","Nat","Neg.neg","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Real","Real.exp","Real.instMul","Real.instNeg","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Submodule.smul","Subtype","instHMul","instHSMul","instLENat","instOfNatNat","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSpectralEvolution","name":"GinibrePoincare.polynomialSpectralEvolution_eigenfunction","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instSemiring","Complex.ofReal","DFunLike.coe","Eq","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.polynomialSpectralEvolution","GinibrePoincare.sumRadiusPolynomialSpace","HMul.hMul","LE.le","LinearMap","LinearMap.instFunLike","Membership.mem","Module.Basis","Module.Basis.instFunLike","Nat","Neg.neg","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Real","Real.exp","Real.instMul","Real.instNeg","RingHom.id","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","instHMul","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","Algebra.id","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instSemiring","Complex.ofReal","DFunLike.coe","DistribMulAction.toMulAction","Eq","Eq.mpr","Eq.refl","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.PolynomialEigenfunctionData","GinibrePoincare.PolynomialEigenfunctionData.a","GinibrePoincare.PolynomialEigenfunctionData.b","GinibrePoincare.PolynomialEigenfunctionData.m","GinibrePoincare.eigenvalue","GinibrePoincare.polynomialEigenfunction","GinibrePoincare.polynomialEigenfunctionBasis","GinibrePoincare.polynomialEigenfunctionBasis_apply","GinibrePoincare.polynomialSpectralEvolution","GinibrePoincare.polynomialSpectralEvolution_basis","GinibrePoincare.sumRadiusPolynomialSpace","HMul.hMul","HSMul.hSMul","IsScalarTower.right","LE.le","LinearMap","LinearMap.instFunLike","Membership.mem","Module.Basis","Module.Basis.instFunLike","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","Neg.neg","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.isScalarTower","Real","Real.exp","Real.instMul","Real.instNeg","RingHom.id","SemigroupAction.toSMul","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submod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able","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.instSFiniteProdVolume","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.integrable_comp_of_integrable","MeasureTheory.MeasurePreserving.integral_comp","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","OrderTop.toTop","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.borelSpace","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.seminormedAddCommGroup","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","Prod","Prod.borelSpace","Prod.fst","Prod.instAddCommMonoid","Prod.instMeasurableSpace","Prod.instModule","Prod.mk","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.Ioo","Set.instLE","Set.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","TopologicalSpace.instSecondCountableTopologyProd","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","abs","abs_nonneg","congrArg","contDiff_prodMk_left","continuous_const","continuous_fst","continuous_id'","deriv","fderiv","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instCountableFin","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalAddGroupReal","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instProperSpaceReal","instSecondCountableTopologyReal","instTopENat","instTopologicalSpaceProd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","instZeroENat","le_abs_self","le_of_not_gt","locallyCompact_of_proper","lt_of_not_ge","measureSpaceOfInnerProductSpace","neg_abs_le","neg_neg_of_pos","not_false_eq_true","of_eq_true","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper","tsupport","tsupport_comp_subset_preimage"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevLineRemovability","name":"GinibrePoincare.polynomial_collision_line_weak_identity_ae","type_dependencies":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","CommSemiring.toSemiring","Complex","Complex.addCommGrou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iteMode_uncentered_eq_centered","GinibrePoincare.transformedCenteredObservableL2","GinibrePoincare.uncenteredGroundStateL2","HAdd.hAdd","HPow.hPow","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","congrArg","id","instAddNat","instHAdd","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.ConcreteTheoremOneNine","name":"GinibrePoincare.positiveHermiteMode_uncentered_eq_centered","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.transformedCenteredObservableL2","GinibrePoincare.uncenteredGroundStateL2","HAdd.hAdd","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeClosedSpan","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection._proof_1","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_1","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_2","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_4","GinibrePoincare.ComplexHermite.hermiteAntiDegreeSpan._proof_5","GinibrePoincare.ComplexHermite.hermiteL2Family._proof_1","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.gaussianHermiteMode_cross_eq_zero","GinibrePoincare.gaussianHermiteMode_eq_antiDegreeProjection","GinibrePoincare.normalizedVandermondeGroundStateL2","GinibrePoincare.normalizedVandermondeGroundStateL2_mem_hermiteAntiDegreeClosedSpan","GinibrePoincare.smoothGinibreMean","GinibrePoincare.transformedCenteredObservableL2","GinibrePoincare.uncenteredGroundStateL2","GinibrePoincare.uncenteredGroundStateL2_eq_centered_add_groundState","HAdd.hAdd","HSMul.hSMul","Iff.mpr","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp"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o","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"],"value_dependencies":["And","Complex","Complex.instNormedField","Complex.instZero","Exists","Fin","GinibrePoincare.Configuration","HasCompactSupport","IsCompact","LE.le","LT.lt","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightPairing","name":"GinibrePoincare.positiveWeightCompactPairing._proof_10","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","MeasurableSet","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","tsupport"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.borelSpace","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","IsClosed.measurableSet","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCountableFin","isClosed_tsupport","secondCountable_of_proper","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightPairing","name":"GinibrePoincare.positiveWeightCompactPairing._proof_11","type_dependencies":["And","Classical.choose","Complex","Complex.instNormedField","Complex.instZero","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.positiveWeightCompactPairing._proof_1","HasCompactSupport","IsCompact","LE.le","LT.lt","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"],"value_dependencies":["And","And.left","Classical.choose","Complex","Complex.instNormedField","Complex.instZero","Exists","Fin","GinibrePoincare.Configuration","HasCompactSupport","IsCompact","LE.le","LT.lt","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightPairing","name":"GinibrePoincare.positiveWeightCompactPairing._proof_12","type_dependencies":["And","Classical.choose","Complex","Complex.instNormedField","Complex.instZero","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.positiveWeightCompactPairing._proof_1","HasCompactSupport","IsCompact","LE.le","LT.lt","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"],"value_dependencies":["And","And.right","Classical.choose","Complex","Complex.instNormedField","Complex.instZero","Exists","Fin","GinibrePoincare.Configuration","HasCompactSupport","IsCompact","LE.le","LT.lt","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightPairing","name":"GinibrePoincare.positiveWeightCompactPairing._proof_13","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.borelSpace",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iv","WithLp.instAddCommGroup","WithLp.instDistribMulAction","WithLp.instModule","WithLp.instSMul","WithLp.ofLp","WithTop.some","Zero.toOfNat0","closure","congr","congrArg","congrFun'","continuous_fst","continuous_pi","continuous_snd","fact_one_le_two_ennreal","fderiv","funext","id","instArchimedeanNat","instCountableFin","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHSMul","instInhabitedNat","instInnerProductSpaceRealComplex","instIsDirectedOrder","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopENat","instTopologicalSpaceProd","isClosed_closure","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","rfl","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevLocalIntegrability","name":"GinibrePoincare.positive_density_integrable_locallyIntegrable","type_dependencies":["BorelSpace","Continuous","ENNReal.ofReal","LT.lt","LocallyCompactSpace","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instZero","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","T2Space","TopologicalSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","BorelSpace","BorelSpace.opensMeasurable","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Continuous","Continuous.inv\u2080","Continuous.measurable","Decidable.decide","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.ofReal","ENNReal.ofReal_lt_top","ENNReal.toReal","ENNReal.toReal_ofReal","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Filter.Eventually.of_forall","Filter.univ_mem'","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HSMul.hSMul","Iff.mp","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsTopologicalDivisionRing.toContinuousInv\u2080","LT.lt","List.nil","LocallyCompactSpace","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Measurable.ennreal_ofReal","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.locallyIntegrable","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.congr","MeasureTheory.LocallyIntegrable.mul_continuous","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.withDensity","MeasureTheory.ae","MeasureTheory.integrable_withDensity_iff_integrable_smul'","Membership.mem","Module.toDistribMulAction","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NeZero.one","Neg.neg","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instInv","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","Pseu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ientProjection_idempotent","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","DFunLike.coe","DFunLike.congr_fun","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","Eq.mpr","EquivLike.toFunLike","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.planarPiBergmanProjection_idempotent","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialHolomorphicQuotientProjection_gauge","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.injective","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume"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omplex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.trans","False","False.elim","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.configurationVolume","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.planarPiBergmanProjection_commutes_globalPhase","GinibrePoincare.potentialGlobalPhaseL2","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","GinibrePoincare.unitary_conjugate_projection_intertwines","GinibrePoincare.vandermondeDegree","GinibrePoincare.volumeGlobalPhaseL2","GinibrePoincare.volumeGlobalPhaseL2_potentialVandermonde","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometry.toContinuousLinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormMulClass.toNoZeroDivisors","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instFloorRing","Real.instOne","Real.instRCLike","Real.instRing","Real.instZero","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","instAddNat","instHAdd","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","isReduced_of_noZeroDivisors","measureSpaceOfInnerProductSpace","norm_zero","pow_ne_zero","zero_ne_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialQuotientProjection","name":"GinibrePoincare.potentialHolomorphicQuotientProjection_residual_norm","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","EquivLike.toFunLike","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace.pi","MeasureTheor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egativeClosure","name":"GinibrePoincare.potentialHolomorphicQuotient_centered_mem_positive","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetric","GinibrePoincare.Potential","GinibrePoincare.potentialCenteredL2","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPositivePhaseClosedSpan","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq.mp","EquivLike.toFunLike","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetric","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.potentialCenteredL2","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialHolomorphicQuotientProjection_centered_orthogonal_constant","GinibrePoincare.potentialHolomorphicQuotient_centered_gauge_mem_alternated_closure","GinibrePoincare.potentialInverseAlternatedClosure_mem_nonnegative","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialNonnegativePhaseClosedSpan","GinibrePoincare.potentialNonnegativePhase_mem_positive_of_orthogonal_constant","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","LinearIsometryEquiv.symm_apply_apply","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","congrArg","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialQuotientNonnegativeClosure","name":"GinibrePoincare.potentialInverseAlternatedClosure_mem_nonnegative","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","EquivLike.toFunLike","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.planarPiAlternatedWeightedMonomialVectors","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialNonnegativePhaseClosedSpan","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instIsBoundedSMul","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Module.toDistr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TopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","map_zero","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialAlternatedPhaseClassification","name":"GinibrePoincare.potentialInverseAlternatedVector_positive_or_bottom_or_zero","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","And","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instCommSemiring","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","EquivLike.toFunLike","Exists","Filter.EventuallyEq","Fin","Fin.fintype","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.IsAlternatingConfigurationPolynomial","GinibrePoincare.IsRotationalPotential","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.planarPiAlternatedWeightedMonomialVectors","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPiVandermondeL2Equiv","GinibrePoincare.potentialPositivePhaseVectors","GinibrePoincare.vandermondeDegree","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.IsHomogeneous","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","SetLike.instMembership","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instDecidableEq","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.semiring","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.zero","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDecidableEq","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","DFunLike.coe","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder"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.Analysis.NonQuadraticPotential","name":"GinibrePoincare.potentialMeasure_isProbabilityMeasure","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","LT.lt","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialMeasure_univ","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPartition_pos","LT.lt","MeasurableSpace.pi","MeasureTheory.IsProbabilityMeasure.mk","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPotential","name":"GinibrePoincare.potentialMeasure_quadratic","type_dependencies":["Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.potentialMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","OfNat.ofNat","Real","Real.semiring","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommMagma.toMul","CommSemigroup.toCommMagma","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.inv_mul_cancel","ENNReal.mul_inv","ENNReal.ofReal","ENNReal.ofReal_ne_top","ENNReal.ofReal_pos","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure._proof_1","GinibrePoincare.ginibreNormalizingMass","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.rawGinibreMeasure","GinibrePoincare.rawGinibreMeasure_eq_scalar_rawPotential","GinibrePoincare.rawPotentialMeasure","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mpr","Inv.inv","IsOrderedAddMonoid.toAddLeftMono","IsScalarTower.left","IsScalarTower.right","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instMulActionOfIsScalarTowerENNReal","MeasureTheory.Measure.instSMul","Monoid.toMulAction","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulAction.toSemigroupAction","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Ne","NeZero.charZero_one","NonUnitalCommSemiring.toCommSemigroup","OfNat.ofNat","One.toOfNat1","Or.inl","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.pi","Real.pi_pos","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","Semiring.toMonoid","Semiring.toMonoidWithZero","Set","Set.univ","Top.top","Zero.toOfNat0","congrArg","div_pos","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","i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incare.potentialMeasure","GinibrePoincare.potentialNonnegativePhaseClosedSpan._proof_1","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPositivePhaseClosedSpan","LT.lt","Lattice.toSemilatticeSup","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","SemilatticeSup.toMax","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.completeLattice","Subtype","Top.top","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialNonnegativePhaseGeometry","name":"GinibrePoincare.potentialNonnegativePhaseClosedSpan._proof_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoid.toAddSubsemigroup","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.carrier","AddZero.toAdd","AddZeroClass.toAddZero","ClosedSubmodule.toSubmodule","CompleteLattice.toConditionallyCompleteLattice","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ConditionallyCompleteLattice.toLattice","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.potentialConstantSpace","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPositivePhaseClosedSpan","InnerProductSpace.toNormedSpace","IsClosed","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Lattice.toSemilatticeSup","Max.max","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","SemilatticeSup.toMax","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.completeLattice","Submodule.toAddSubmonoid","Subtype","Top.top","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoid.toAddSubsemigroup","AddSubmonoidClass.toAddCommMonoid","AddSubsemigroup.carrier","AddZero.toAdd","AddZeroClass.toAddZero","ClosedSubmodule.isClosed","ClosedSubmodule.toSubmodule","CompleteLattice.toConditionallyCompleteLattice","Complex","Complex.addGroupWithOne","Complex.instAddComm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ormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","Eq.refl","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialNonnegativePhaseClosedSpan","GinibrePoincare.potentialPartition","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialNonnegativePhaseGeometry","name":"GinibrePoincare.potentialNonnegativePhase_mem_positive_of_orthogonal_constant","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.potentialConstantL2","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialNonnegativePhaseClosedSpan","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPositivePhaseClosedSpan","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.to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asurable","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.continuous_normSq","Complex.continuous_ofReal","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.normSq_nonneg","Complex.ofReal","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","Continuous.div_const","Continuous.measurable","Continuous.mul","Continuous.norm","Continuous.pow","ContinuousENorm.toENorm","ContinuousMul.measurableMul\u2082","DFunLike.coe","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.lt_top_of_mul_ne_top_right","ENNReal.ofReal","ENNReal.ofReal_mul","ENNReal.ofReal_pos","Eq","Eq.mp","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Fin","Fin.val","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPotentialHalfWeight","GinibrePoincare.planarWeightedMonomial_norm_sq","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPolynomialVolume","GinibrePoincare.potentialPolynomialVolume.eq_1","GinibrePoincare.rawPotentialKostlanCoordinateLaw","GinibrePoincare.rawPotentialKostlanCoordinateLaw_eq_volume","GinibrePoincare.rawPotentialKostlanCoordinateLaw_mass_valid","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","LT.lt.ne","LT.lt.ne'","Lattice.toSemilatticeInf","Measurable.ennreal_ofReal","Measurable.pow_const","MeasurableSet.univ","MeasureTheory.AEStronglyMeasurable","MeasureTheory.HasFiniteIntegral","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_univ","MeasureTheory.Measure.smul_apply","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.ae_of_all","MeasureTheory.hasFiniteIntegral_iff_ofReal","MeasureTheory.lintegral","MeasureTheory.lintegral_withDensity_eq_lintegral_mul","MeasureTheory.memLp_two_iff_integrable_sq_norm","MeasureTheory.withDensity_apply","MetricSpace.toEMetricSpace","Monoid.measurablePow","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","Nat.instAtLeastTwoHAddOfNat","Nat.instMeasurableSpace","Nat.instNeZeroSucc","Ne","NeZero.charZero_one","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instMul","Pi.instPow","Pi.instZero","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.continuous_exp","Real.exp","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.normedCommRing","Real.partialOrder","Real.pi","Real.pi_pos","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.t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edRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialPositivePhaseClosure","name":"GinibrePoincare.potentialPositivePhaseClosedSpan._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_1","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_2","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialPositivePhaseClosure","name":"GinibrePoincare.potentialPositivePhaseClosedSpan._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_1","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_2","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_3","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_5","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_6","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_7","GinibrePoincare.potentialPositivePhaseClosedSpan._proof_8","GinibrePoincare.potentialPositivePhaseVectors","IsClosed","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.coe","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.span","Submodule.topologicalClosure","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSub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IsScalarTower.right","Measurable.aemeasurable","Measurable.of_eval","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instAddCommMonoid","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.integral","MeasureTheory.integral_finsetSum_measure","MeasureTheory.integral_map","MeasureTheory.integral_smul_measure","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semiring.toMonoid","SetLike.instMembership","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","congrArg","congrFun'","id","instCountableFin","instDecidableEqFin","instDistribOfSemiring","instHMul","instHSMul","instSMulOfMul","instSecondCountableTopologyReal","measurable_pi_apply","rfl","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialSymmetrizedLaw","name":"GinibrePoincare.potentialSymmetrizedRadiusProduct_integral_symmetric","type_dependencies":["Eq","Fin","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.potentialRadiusProduct","GinibrePoincare.potentialSymmetrizedRadiusProduct","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure","MeasureTheory.integral","Nat","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instRCLike","Real.measurableSpace","Real.norm","Real.normedAddCommGroup"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","BorelSpace.opensMeasurable","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toInv","DivisionSemiring.toGroupWithZero","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.toReal","ENNReal.toReal_inv","ENNReal.toReal_natCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Equiv.Perm","Equiv.inhabited'","Equiv.instEquivLike","Equiv.instFintype","EquivLike.toFunLike","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.univ","Fintype.card","Fintype.card_ne_zero","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.potentialRadiusProduct","GinibrePoincare.potentialSymmetrizedRadiusProduct","GinibrePoincare.potentialSymmetrizedRadiusProduct._proof_1","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HMul.hMul","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","IsScalarTower.right","LE.le","Measurable","Measurable.aemeasurable","Measurable.aestronglyMeasurable","Measurable.of_eval","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.mono'","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instAddCommMonoid","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.isFiniteMeasure_map","MeasureTheory.Measure.map","MeasureTheory.ae","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_finsetSum_measure","MeasureTheory.integral_map","MeasureTheory.integral_smul_measure","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NSMul.toSMul","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_zero","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedR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roup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Continuous","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.Potential","GinibrePoincare.configurationVolume","GinibrePoincare.configurationVolume_absolutelyContinuous_potentialMeasure","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialVandermondeMultiplier","GinibrePoincare.potentialVandermonde_memLp","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.pseudoMetricSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","Top.top","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralPotentialVandermondeL2","name":"GinibrePoincare.potentialVandermondeL2._proof_3","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.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inibrePoincare.Potential","GinibrePoincare.piCompactWeightedDbarGraph","GinibrePoincare.planarPiBergmanProjection","GinibrePoincare.potentialGradientEnergy","GinibrePoincare.potentialPartition","GinibrePoincare.potentialVandermondeCoefficient","GinibrePoincare.potentialVandermondeCoefficient_contDiff","GinibrePoincare.potentialVandermondeCoefficient_hasCompactSupport","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","Prod.fst","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Bool","Bool.false","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.normSq","Complex.ofReal","Complex.ofRealCLM","Complex.ofReal_zero","ContDiff","ContDiff.comp","ContDiff.continuous","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.contDiff","ContinuousLinearMap.funLike","DFunLike.coe","Decidable.byContradiction","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FiniteDimensional.rclike_to_real","Finset.sum","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.PlanarPiDbarGraphSpace","GinibrePoincare.PlanarPiDbarGraphSpace._proof_1","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.configura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otentialSquaredRadiusProfile","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","InvOneClass.toOne","IsOrderedAddMonoid.toAddLeftMono","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toMul","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNormedAddGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNorm","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Not","OfNat.ofNat","One.toOfNat1","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instMonoid","Real.instOne","Real.instPreorder","Real.instZero","Real.lattice","Real.norm","Real.norm_eq_abs","Real.semiring","Real.sqrt","Real.sqrt_sq","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","abs","abs_of_nonneg","congr","congrArg","dite","div_mul_cancel\u2080","div_self","eq_self","id","instHDiv","instHMul","instHPow","instMulZeroOneClassOfSemiring","instOfNatNat","norm_div","norm_ne_zero_iff","norm_nonneg","norm_zero","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialEntropyTransfer","name":"GinibrePoincare.potential_magnitude_entropy_eq_radiusProduct","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.magnitudeVector","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialRadiusProduct","GinibrePoincare.squareEntropy","LE.le","LT.lt","MeasurableSpace.pi","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.lattice","Real.measurableSpace","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","abs","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddGroup","And","CommRing.toNonUnitalCommRing","CompactIccSpace.isCompact_Icc","Complex","Complex.instNormedField","Complex.measurableSpace","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.continuousOn","Continuous.pow","DFunLike.coe","DistribLattice.toLattice","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mpr","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.magnitudeVector","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialRadiusProduct","GinibrePoincare.potential_magnitude_expectation_eq_radiusProduct","GinibrePoincare.squareEntropy_eq_of_moments","HMul.hMul","HPow.hPow","Iff.mp","InnerProductSpace.toNormedSpace","IsCompact.exists_bound_of_continuousOn","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","Lattice.toSemilatticeInf","MeasurableSpace.pi","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instConditionallyCompleteLinearOrder","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instRing","Real.lattice","Real.linearOrder","Real.log","Real.measurableSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Set","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","abs","abs_le","abs_nonneg","abs_pow","congrArg","continuous_id","id","instDistribLatticeOfLinearOrder","instHMul","instHPow","instIsTopologicalRingReal","instLTNat","instOfNatNat","instOrderTopologyReal","pow_le_pow_left\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialEntropyTransfer","name":"GinibrePoincare.potential_magnitude_expectation_eq_radiusProduct","type_dependencies":["Complex","Complex.instNormedField","Complex.measurableSpace","Continuous","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.magnitudeVector","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialRadiusProduct","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Nat","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instRCLike","Real.measurableSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["BorelSpace.opensMeasurable","Complex","Complex.instNorm","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.normSq_eq_norm_sq","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","Continuous.measurable","Continuous.sqrt","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv.Perm","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.magnitudeVector","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialRadiusProduct","GinibrePoincare.potentialSquaredRadiusProduct","GinibrePoincare.potentialSquaredRadiusProduct_sqrt_map","GinibrePoincare.potential_radial_expectation_eq_squaredRadiusProduct","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Measurable.aemeasurable","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.integral","MeasureTheory.integral_map","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.borelSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instLE","Real.instMonoid","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.semiring","Real.sqrt","Real.sqrt_sq","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","continuous_apply","continuous_pi","eq_self","funext","id","instCountableFin","instHPow","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat","instSecondCountableTopologyReal","norm_nonneg","of_eq_true","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialGradientTransfer","name":"GinibrePoincare.potential_magnitude_gradient_energy_eq_radiusPr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LE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSemigroup","Real.instSub","Real.normedAddCommGroup","Real.semiring","Semifield.toCommGroupWithZero","Semigroup.toMul","congr","congrArg","congrFun'","div_eq_mul_inv","funext","id","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_assoc","mul_comm","mul_inv_rev","mul_left_comm"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPotential","name":"GinibrePoincare.potential_quadratic_radial_lsi","type_dependencies":["Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRadialFunctionLSI","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.potentialGradientEnergy","GinibrePoincare.potentialMeasure","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","MeasurableSpace.pi","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.semiring","instHDiv","instHMul","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Field.toSemifield","Fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.IsRadialFunctionLSI","GinibrePoincare.IsSmoothCompactSymmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSquareEntropy","GinibrePoincare.potentialGradientEnergy","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialMeasure_quadratic","GinibrePoincare.radial_core_lsi","GinibrePoincare.realGradientNormSq","GinibrePoincare.smoothGinibreEnergy","GinibrePoincare.squareEntropy","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","LE.le","LT.lt","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Zero.toOfNat0","congr","congrArg","congrFun'","ge_iff_le._simp_1","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","one_div","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticKostlan","name":"GinibrePoincare.potential_radial_entropy_eq_product","type_dependencies":["Comp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ulZeroOneClassOfSemiring","instOfNatNat"],"value_dependencies":["CommRing.toNonUnitalCommRing","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous","Continuous.pow","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.trans","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","Fin","Function.comp","Function.support","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.compactSupport_square_mul_log","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","GinibrePoincare.potential_radial_expectation_eq_squaredRadiusProduct","GinibrePoincare.squareEntropy_eq_of_moments","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.exists_bound_of_continuous","HasCompactSupport.mono","InnerProductSpace.toNormedSpace","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instRCLike","Real.instZero","Real.log","Real.measurableSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","instHMul","instHPow","instIsTopologicalRingReal","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat","not_false_eq_true","of_eq_true","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialEntropyTransfer","name":"GinibrePoincare.potential_radial_entropy_eq_squaredRadiusProduct_bounded","type_dependencies":["Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous","DFunLike.coe","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProduct","GinibrePoincare.squareEntropy","LE.le","LT.lt","MeasurableSpace.pi","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instAddGroup","Real.instLE","Real.lattice","Real.measurableSpace","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","abs","instLTNat","instMulZeroOneClassOfSemiring","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","And","CommRing.toNonUnitalCommRing","CompactIccSpace.isCompact_Icc","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous","Continuous.continuousOn","Continuous.pow","DFunLike.coe","DistribLattice.toLattice","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","Eq","Eq.mpr","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.Potential","GinibrePoincare.continuous_square_mul_log","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialSquaredRadiusProdu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otential_coordinates_ne_zero_ae","GinibrePoincare.realGradientNormSq","GinibrePoincare.realGradientNormSq_magnitude","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Ne","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRing","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Set","Set.instMembership","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.prime_X_sub_X","type_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.ring","CommSemiring.toCommMonoidWithZero","Complex","Complex.instCommSemiring","Complex.instRing","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","HSub.hSub","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","Prime","Ring.toAddGroupWithOne","SubNegMonoid.toSub","instHSub"],"value_dependencies":["AddCancelMonoid.toIsCancelAdd","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toAddCancelMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commRing","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","AlgEquiv","AlgEquiv.instAlgEquivClass","AlgEquiv.instEquivLike","AlgEquiv.instFunLike","AlgEquiv.toMulEquiv","AlgEquivClass.toAlgHomClass","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","Algebra.id","Algebra.toModule","CommSemiring.toCommMonoidWithZero","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instCommSemiring","Complex.instField","Complex.instRing","DFunLike.coe","Distrib.toMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mpr","Eq.refl","EquivLike.toFunLike","Field.toSemifield","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.ConfigurationPolynomialAway","GinibrePoincare.asPolynomialInVariable","GinibrePoincare.asPolynomialInVariable_X_of_ne","GinibrePoincare.asPolynomialInVariable_X_self","HSub.hSub","Iff.mp","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidHom","MonoidHom.id","MonoidHom.instFunLike","MulEquiv","MulEquiv.instEquivLike","MulEquiv.instMulEquivClass","MulEquiv.prime_iff","MulOneClass.toMulOne","MulZeroClass.toZero","MvPolynomial","MvPolynomial.X","MvPolynomial.instIsDomainOfIsCancelAdd","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass","NonUnitalNonAssocSemiring.toAddCommMonoid","Polynomial","Polynomial.C","Polynomial.X","Polynomial.algebraOfAlgebra","Polynomial.commSemiring","Polynomial.instSub","Polynomial.prime_X_sub_C","Polynomial.ring","Polynomial.semiring","Prime","Ring.toAddCommGroup","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Subtype","Subtype.mk","congrArg","id","instDistribOfSemiring","instHSub","instIsDomain","map_sub","outParam"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HolomorphicVandermondeDivision","name":"GinibrePoincare.prod_orderedPairFactor","type_dependencies":["AddMonoidAlgebra.commRing","CommRing.toCommMonoid","Complex","Complex.commRing","Eq","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.Subtype.fintype","Finset.instSetLike","Finset.prod","Finset.univ","Finsupp","Finsupp.instAddCommMonoid","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.OrderedParticlePair","GinibrePoincare.orderedPairFactor","GinibrePoincare.polynomialVandermonde","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","SetLike.instMembership","Sigma.instFintype","Subtype"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidAlgebra.commRing","AddMonoidAlgebra.ring","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instRing","Eq","Eq.mpr","Eq.symm","Eq.trans","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.Subtype.fintype","Finset.instSetLike","Finset.mem_Ioi._simp_2","Finset.prod","Finset.prod_congr","Finset.prod_subtype","Finset.uni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ormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat","nhds"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.ndrec","Eq.trans","EquivLike.toFunLike","Exists","Exists.casesOn","Field.toDivisionRing","Filter","Filter.Tendsto","Filter.Tendsto.add","GinibrePoincare.boundedOperators_isClosed_strong_limit","GinibrePoincare.l2ProductCompletedTensorEquiv_sigmaFinite","GinibrePoincare.l2ProductTensorEquiv_coe","GinibrePoincare.l2ProductTensorMap","GinibrePoincare.l2ProductVector","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsClosed.preimage","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LinearIsometryEquiv","LinearIsometryEquiv.continuous","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.surjective","LinearMap","LinearMap.instFunLike","LinearMap.semilinearMapClass","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.prod","MeasureTheory.SigmaFinite","MeasureTheory.instSFiniteOfSigmaFinite","Membership.mem","Module.toDistribMulAction","NNNorm.nnnorm","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomInvPair.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","SemilinearMapClass.distribMulActionSemiHomClass","SemilinearMapClass.toAddHomClass","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddCommGroup.to_isUniformAddGroup","SeminormedAddGroup.toNNNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Se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Group","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.normed","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Filter.mp_mem","Filter.univ_mem'","FiniteDimensional.rclike_to_real","GinibrePoincare.productPlaneL2BumpAverage","GinibrePoincare.productPlaneL2BumpAverage_pairing","GinibrePoincare.productPlaneL2Translate","GinibrePoincare.productPlaneL2Translate_ae","HMul","HMul.hMul","HSub.hSub","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsSimpleModule.instIsNoetherian","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Module.IsNoetherian.finite","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instSub","Prod.instZero","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instCompleteSpace","Real.instDivisionRing","Real.instMul","Real.instRCLike","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","conj_trivial","eq_self","fact_one_le_two_ennreal","id","innerSL","instDistribOfSemiring","instHMul","instHSub","instInnerProductSpaceRealComplex","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inormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHMul","instInnerProductSpaceRealComplex","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instT2Space","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.comp","ContinuousLinearMap.fst","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","ContinuousLinearMap.smul_apply","ContinuousLinearMap.snd","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt.hasFDerivAt","Distrib.toAdd","Distrib.toMul","DistribMulAction.toMulAction","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Function.comp","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","HasFDerivAt.mul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Module.toDistribMulAction","Monoid.toNPow","Monoid.toSemigroup","MulAction.toSemigroupAction","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","Pi.instMul","PolynormableSpace.continuousSMul","Prod","Prod.continuousAdd","Prod.continuousSMul","Prod.fst","Prod.instAddCommGroup","Prod.instModule","Prod.mk","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congr","congrArg","congrFun'","fderiv","hasFDerivAt_fst","hasFDerivAt_snd","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instPolynormableSpace","instSMulOfMul","instTopologicalSpaceProd","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevFubini","name":"GinibrePoincare.product_weak_derivative_identity_of_finite_crossings","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAdd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semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","autoParam","congrArg","congrFun'","dite","funext","id","inferInstance","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instSecondCountableTopologyReal","integrable_rpow_mul_exp_neg_mul_sq","le_of_lt","le_of_not_gt","lt_of_lt_of_le","max_eq_left","mul_le_mul_of_nonneg_left","mul_pos","norm_nonneg","pow_nonneg","pow_pos","rfl","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementDensity_mass_pos","type_dependencies":["GinibrePoincare.radialConfinementDensity","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLT","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","And.left","CommSemiring.toSemiring","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCharZero","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_one","Eq.trans","Function.support","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementDensity_nonneg","GinibrePoincare.radialConfinementDensity_pos","HSub.hSub","Iff.mpr","IsOrderedRing.toZeroLEOneClass","LE.le","LT.lt","LT.lt.ne'","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.integral_pos_iff_support_of_nonneg","MeasureTheory.measure_mono","Membership.mem","Nat","NeZero.charZero_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instLT","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.volume_Ioo","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.Ioo","Set.instLE","Set.instMembership","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","instHSub","lt_of_lt_of_le","of_eq_true","sub_zero","zero_lt_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementDensity_nonneg","type_dependencies":["GinibrePoincare.radialConfinementDensity","LE.le","Nat","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","GinibrePoincare.radialConfinementDensity","HAdd.hAdd","HMul.hMul","HPow.hPow","IsOrderedRing.toPosMulMono","IsOrderedRing.toZeroLEOneClass","LE.le","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.nonneg_of_isNat","Max.max","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Real","Real.exp","Real.exp_pos","Real.instIsOrderedRing","Real.instLE","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semiring.toMonoidWithZero","Zero.toOfNat0","id","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","le_max_of_le_right","le_of_lt","mul_nonneg","pow_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementDensity_pos","type_dependencies":["GinibrePoincare.radialConfinementDensity","LT.lt","Nat","OfNat.ofNat","Real","Real.instLT","Real.instZero","Zero.toOfNat0"],"value_dependencies":["Eq","Eq.mpr","GinibrePoincare.radialConfinementDensity","HAdd.hAdd","HMul.hMul","HPow.hPow","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LT.lt","LT.lt.le","LinearOrder.toMax","Max.max","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Real","Real.exp","Real.exp_pos","Real.instIsStrictOrderedRing","Real.instLT","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semiring.toMonoidWithZero","Zero.toOfNat0","congrArg","id","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","max_eq_left","mul_pos","pow_pos"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLaw","name":"GinibrePoincare.radialConfinementDensity_square_lintegral","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","GinibrePoincare.radialConfinementDensity","HMul.hMul","HPow.hPow","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","OfNat.ofNat","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instZero","Real.measureSpace","Real.sqrt","Set.Ioi","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Bool","Bool.false","Bool.true","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.ofNat_ne_top","ENNReal.ofReal","ENNReal.ofReal_mul","ENNReal.ofReal_ofNat","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.radialConfinementDensity","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivWithinAt","HasDerivWithinAt.congr_simp","HasDistribNeg.toInvolutiveNeg","HasSolidNorm.orderClosedTopology","Iff.intro","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","InvolutiveNeg.toNeg","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsModuleTopology.toContinuousSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toMax","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Max.max","MeasureTheory.Measure","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","MeasureTheory.lintegral_const_mul'","MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul","MeasureTheory.setLIntegral_congr_fun","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMonoid","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","Not.intro","OfNat.ofNat","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMax","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_pos","Real.sqrt_sq_eq_abs","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SemilatticeInf.toPartialOrder","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.InjOn","Set.Ioi","Set.ext","Set.image","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_pos","addRightReflectLE_of_addLeftReflectLE","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","hasDerivWithinAt_pow","id","inferInstance","instAddNat","instClosedIicTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalRingReal","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSubNat","le_of_lt","max_eq_left","measurableSet_Ioi","mul_assoc","mul_pos","mul_pos_of_neg_of_neg","neg_eq_zero","neg_mul","pow_add","pow_mul","pow_one","pow_pos","rfl","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analy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commRing","Real.continuous_sqrt","Real.decidableLT","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMonoid","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.sqrt","Real.sqrt_sq_eq_abs","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_pos","congrArg","congrFun'","eq_self","id","instHDiv","instHPow","instIsTopologicalRingReal","instOfNatNat","instSecondCountableTopologyReal","le_of_not_gt","measurable_id'","of_eq_true","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementProbabilityDensity_hasDerivAt","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Differentiable","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.radialConfinementProbabilityDensity","GinibrePoincare.radialEffectivePotential","HAdd.hAdd","HMul.hMul","HasDerivAt","IsModuleTopology.toContinuousSMul","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","LT.lt","Module.toDistribMulAction","Nat","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instLT","Real.instMul","Real.instNeg","Real.instZero","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","instAddNat","instHAdd","instHMul","instIsTopologicalRingReal","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt","DifferentiableAt.const_mul","DifferentiableAt.hasDerivAt","DifferentiableAt.sub","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementDensity_eq_exp","GinibrePoincare.radialConfinementProbabilityDensity","GinibrePoincare.radialConfinementProbabilityDensity.eq_1","GinibrePoincare.radialEffectivePotential","GinibrePoincare.radialEffectivePotential._proof_1","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasDerivAt","HasDerivAt.congr_deriv","HasDerivAt.congr_of_eventuallyEq","HasDerivAt.div_const","HasDerivAt.exp","HasDerivAt.neg","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.toNormedRing","NormedField.toField","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instNeg","PolynormableSpace.continuousSMul","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.differentiableAt_log","Real.exp","Real.instAddCommGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.log","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","deriv","eventually_gt_nhds","id","inferInstance","instAddNat","instClosedIicTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instHasSolidNormReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","nhds","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementProbabilityDensity_integral","type_dependencies":["Eq","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementProbabilityDensity","InnerProductSpace.toNormedSpace","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instOne","Real.instRCLike","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["DenselyNormedField.toNormedField","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementDensity_mass_pos","GinibrePoincare.radialConfinementProbabilityDensity","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HDiv.hDiv","InnerProductSpace.toNormedSpace","InvOneClass.toOne","LT.lt.ne'","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MeasureTheory.integral_div","Nat","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instField","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","div_self","id","instHDiv"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementProbabilityDensity_isProbability","type_dependencies":["Continuous","ENNReal.ofReal","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementProbabilityDensity","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.measureSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["BorelSpace.opensMeasurable","Continuous","Continuous.measurable","DFunLike.coe","ENNReal","ENNReal.instOne","ENNReal.ofReal","ENNReal.ofReal_one","Eq","Eq.mpr","Eq.symm","Eq.trans","Filter.Eventually.of_forall","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementProbabilityDensity","GinibrePoincare.radialConfinementProbabilityDensity_continuous","GinibrePoincare.radialConfinementProbabilityDensity_integral","GinibrePoincare.radialConfinementProbabilityDensity_nonneg","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSet.univ","MeasureTheory.Integrable","MeasureTheory.Integrable.div_const","MeasureTheory.IsProbabilityMeasure.mk","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_univ","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.lintegral","MeasureTheory.ofReal_integral_eq_lintegral_ofReal","MeasureTheory.withDensity_apply","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","Pi.instZero","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instLE","Real.instOne","Real.instRCLike","Real.instZero","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.univ","True","True.intro","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","eq_true","id","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialDensity","name":"GinibrePoincare.radialConfinementProbabilityDensity_nonneg","type_dependencies":["GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementProbabilityDensity","LE.le","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.measureSpace","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["DivisionSemiring.toGroupWithZero","Field.toSemifield","GinibrePoincare.radialConfinementDensity","GinibrePoincare.radialConfinementDensity_mass_pos","GinibrePoincare.radialConfinementDensity_nonneg","InnerProductSpace.toNormedSpace","IsStrictOrderedRing.toPosMulStrictMono","LT.lt.le","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","MulZeroClass.toMul","MulZeroClass.toZero","Nat","NonUnitalSeminormedCommRing.toNonUnitalS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incare.Configuration","GinibrePoincare.ginibreSpatialCutoff","HAdd.hAdd","HSMul.hSMul","Nat","Nat.cast","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","RCLike.toNormedAlgebra","Real","Real.instAdd","Real.instNatCast","Real.instOne","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instHAdd","instHSMul","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMollifierKernels","name":"GinibrePoincare.radialMollifierBase.eq_1","type_dependencies":["Algebra.toSMul","Complex","Complex.instNormedField","Complex.instRCLike","Eq","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreSpatialCutoff","GinibrePoincare.radialMollifierBase","HAdd.hAdd","HSMul.hSMul","Nat","Nat.cast","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","RCLike.toNormedAlgebra","Real","Real.instAdd","Real.instNatCast","Real.instOne","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instHAdd","instHSMul","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierBase","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMollifierKernels","name":"GinibrePoincare.radialMollifierBase_compact","type_dependencies":["Complex","Complex.instNormedField","Fin","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierBase","HasCompactSupport","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Algebra.toSMul","Bool","Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","DistribMulAction.toMulAction","DivisionSemiring.toGroupWithZero","Eq.refl","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.ginibreSpatialCutoff","GinibrePoincare.ginibreSpatialCutoff_compact","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HSMul.hSMul","HasCompactSupport.comp_isClosedEmbedding","Homeomorph.isClosedEmbedding","Homeomorph.smulOfNeZero","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Module.toDistribMulAction","Monoid.toSemigroup","MonoidWithZero.toMonoid","MulAction.toSemigroupAction","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.mulAction","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instContinuousConstSMulForall","instHAdd","instHSMul","instInnerProductSpaceRealComplex","instOfNatNat","ne_of_gt"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMollifierKernels","name":"GinibrePoincare.radialMollifierBase_integrable","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierBase","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","BorelSpace.opensMeasurable","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instCompleteSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","ContDiff.continuous","Continuous.integrable_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierBase","GinibrePoincare.radialMollifierBase_compact","GinibrePoincare.radialMollifierBase_smooth","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instIsFiniteMeasureOnCompactsForallVolumeOfSigmaFinite","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MetricSpace.toEMetricSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","T6Space.toT0Space","Top.top","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop.some","instCountableFin","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","instTopENat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMollifierKernels","name":"GinibrePoincare.radialMollifierBase_mass_pos","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.radialMollifierBase","InnerProductSpace.toNormedSpace","LT.lt","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instLT","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Zero.toOfNat0","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CharP.cast_eq_zero","CharP.ofCharZero","CommGroupWithZero.toDivisionCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.normSq","ContDiff.continuous","ContDiffBump","ContDiffBump.one_of_mem_closedBall","ContDiffBump.toFun","ContDiffBump.toFun.congr_simp","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENat","Eq","Eq.refl","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","False","Field.toSemifield","Fin","Fin.fintype","Finite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oidWithOne.toNatCast","AddMonoidWithOne.toOne","And","And.casesOn","And.intro","And.left","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","Continuous.intervalIntegrable","DFunLike.coe","DistribLattice.toLattice","DivInvMonoid.toDiv","ENNReal","ENNReal.instZero","ENNReal.ofReal","ENormedAddMonoid.toESeminormedAddMonoid","ESeminormedAddMonoid.toContinuousENorm","EmptyCollection.emptyCollection","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.radialPowerMeasure","HAdd.hAdd","HDiv.hDiv","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff","Iff.intro","InnerProductSpace.toNormedSpace","Inter.inter","IsOrderedRing.toPosMulMono","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","LE.le.trans","LT.lt","LT.lt.le","LT.lt.ne'","Lattice.toSemilatticeInf","MeasureTheory.IntegrableOn","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instZero","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_empty","MeasureTheory.Measure.restrict_restrict","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.ae_restrict_mem","MeasureTheory.integral","MeasureTheory.lintegral","MeasureTheory.lintegral_zero_measure","MeasureTheory.ofReal_integral_eq_lintegral_ofReal","MeasureTheory.withDensity_apply","Membership.mem","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_add._simp_1","Nat.cast_inj._simp_1","Nat.cast_one","Nat.instPreorder","Nat.sub_add_cancel","Nat.succ","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toENormedAddMonoid","NormedField.toNormedSpace","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instZero","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.decidableLE","Real.instAdd","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.locallyFinite_volume","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Iic","Set.Ioc","Set.Ioi","Set.ext","Set.instEmptyCollection","Set.instInter","Set.instMembership","Set.mem_Iic._simp_2","Set.mem_Ioc._simp_1","Set.mem_Ioi._simp_1","Set.mem_inter_iff._simp_1","Set.ofPred","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.HomogeneousRadialMeasure.0.GinibrePoincare.radialPowerMeasure_Iic._simp_1_1","_private.GinibrePoincare.Analysis.HomogeneousRadialMeasure.0.GinibrePoincare.radialPowerMeasure_Iic._simp_1_2","_private.GinibrePoincare.Analysis.HomogeneousRadialMeasure.0.GinibrePoincare.radialPowerMeasure_Iic._simp_1_3","_private.GinibrePoincare.Analysis.HomogeneousRadialMeasure.0.GinibrePoincare.radialPowerMeasure_Iic._simp_1_4","_private.GinibrePoincare.Analysis.HomogeneousRadialMeasure.0.GinibrePoincare.radialPowerMeasure_Iic._simp_1_5","cast","congr","congrArg","congrFun'","continuous_pow","dite","eq_self","id","if_neg","if_pos","iff_false","instAddNat","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHPow","instHSub","instHasSolidNormReal","instIsTopologicalRingReal","instLTNat","instOfNatNat","instSubNat","integral_pow","intervalIntegral","intervalIntegral.integral_of_le","ite","le_of_not_ge","measurableSet_Iic","measurableSet_Ioc","not_lt_of_ge","of_eq_true","pow_nonneg","sub_zero","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.HomogeneousRadialMeasure","name":"GinibrePoincare.radialPowerMeasure_gaussian_tilt","type_dependencies":["Algebra.id","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","GinibrePoincare.radialPowerMeasure","HSMul.hSMul","IsScalarTower.right","LT.lt","MeasureTheory.Measure","MeasureTheory.Measure.instSMul","MeasureTheory.Measure.withDensity","Nat","Nat.cast","Neg.neg","OfNat.ofNat","One.toOfNat1","ProbabilityTheory.gammaM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rePoincare.radialSobolevDomain","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Exists","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevClosure","GinibrePoincare.radialSobolevDomain._proof_1","GinibrePoincare.radialSobolevDomain._proof_2","GinibrePoincare.radialSobolevDomain._proof_3","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevSpace","name":"GinibrePoincare.radialSobolevDomain._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevSpace","name":"GinibrePoincare.radialSobolevDomain._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevSpace","name":"GinibrePoincare.radialSobolevDomain._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","IsTopologicalAddGroup","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","fact_one_le_two_ennreal","instFintypeProd","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevSpace","name":"GinibrePoincare.radialSobolevDomain_lsi","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.measurableSpace","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","EuclideanSpace","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevDomain","GinibrePoincare.radialSobolevGradient","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheor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SobolevCorePairs","GinibrePoincare.radialSobolevCorePairs._proof_1","GinibrePoincare.radialSobolevCorePairs._proof_2","GinibrePoincare.radial_compact_phaseRegular_weak_mem_sobolevClosure","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasCompactSupport","HasCompactSupport.mul_left","InnerProductSpace.toNormedSpace","IsClosed.mem_of_tendsto","IsTopologicalAddGroup.toContinuousAdd","LE.le","LE.le.trans","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.congr","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.aestronglyMeasurable","MeasureTheory.Lp.coeFn_add","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommGroup","Pi.instAdd","Pi.instMul","Pi.topologicalSpace","PiLp.innerProductSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PiLp.normedSpace","PiLp.seminormedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instAddCommGroup","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instZero","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","WithLp.instSMul","Zero.toOfNat0","add_zero","closure","congr","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instArchimedeanNat","instFintypeProd","instHAdd","instHMul","instHSMul","instInhabitedNat","instIsDirectedOrder","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceProd","isClosed_closure","nhds","of_eq_true","tsupport","tsupport_mul_subset_left"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialBoundedWeakSobolevApproximation","name":"GinibrePoincare.radial_bounded_weak_exists_core_sequence","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevCorePairs","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instZero","Real.norm","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.instMembership","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instMulZe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rePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevCorePairs","GinibrePoincare.radial_compact_interior_weak_mem_sobolevClosure","HasCompactSupport","Iff.mp","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MetricSpace.toEMetricSpace","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","TopologicalSpace.instFirstCountableTopologyProd","UniformSpace.toTopologicalSpace","closure","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceProd","mem_closure_iff_seq_limit","nhds","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreWeakGradientSupport","name":"GinibrePoincare.radial_compact_interior_weak_lsi","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSquareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","HasCompactSupport","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","PseudoMetricSpace.toUniformSpace","Real","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instZero","Real.log","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHDiv","instHMul","instHPow","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.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"module":"GinibrePoincare.Analysis.RadialPhaseWeakSobolevApproximation","name":"GinibrePoincare.radial_compact_phaseRegular_weak_mem_sobolevClosure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.PhaseRegular","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevClosure","HasCompactSupport","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","And.casesOn","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Exists.casesOn","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.Tendsto","Filter.atTop","Filter.atTop_neBot","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.PhaseRegular","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibre_distributional_gradient_exists_supported_representative","GinibrePoincare.radialSobolevClosure","GinibrePoincare.radialSobolevCorePairs","GinibrePoincare.radial_phaseRegular_weak_exists_core_sequence","HasCompactSupport","IsClosed.mem_of_tendsto","LE.le","LE.le.trans","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NegZeroClass.toZero","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.addCommGroup","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommGroup","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithLp.instAddCommGroup","closure","fact_one_le_two_ennreal","instArchimedeanNat","instFintypeProd","instInhabitedNat","instIsDirectedOrder","instLTNat","instMulZeroOneClassOfSemiring","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat"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oAddMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.measurableSpace","Complex.ofReal","Continuous","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Differentiable","DistribMulAction.toMulAction","Eq","Field.toSemifield","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","MeasureTheory.integral","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMonoid","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instDenselyNormedField","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","Complex.ofReal","Continuous","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Differentiable","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.mpr","Eq.trans","Field.toSemifield","GinibrePoincare.radial_integral_holomorphic_mean_value","HSMul.hSMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","MeasureTheory.convolution_lsmul","MeasureTheory.integral","Module.toDistribMulAction","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedAlgebra.toAlgebra","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMonoid","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","congrArg","congrFun'","funext","id","instHSMul","instHSub","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace","one_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialConvolutionInvariance","name":"GinibrePoincare.radial_coordinatePhase","type_dependencies":["Complex","Complex.instNorm","Complex.instSemiring","Complex.normSq","DFunLike.coe","Eq","Exists","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinatePhase","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.semiring","instMulZeroOneClassOfSemiring"],"value_dependencies":["Complex","Complex.instMul","Complex.instNorm","Complex.instSemiring","Complex.normSq","Complex.norm_mul","DFunLike.coe","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.trans","Exists","Exists.casesOn","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinatePhas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italNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toDivisionRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","OpenPartialHomeomorph.symm","OpenPartialHomeomorph.toFun'","OpenPartialHomeomorph.toPartialHomeomorph","PartialEquiv.target","PartialHomeomorph.toPartialEquiv","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","Prod","Prod.fst","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommMonoid","Real.instIsOrderedAddMonoid","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.measureSpace","Real.normedAddCommGroup","Real.normedField","Real.pi","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","SProd.sprod","Semifield.toCommSemiring","SemigroupAction.toSMul","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","Set.Ioi","Set.Ioo","Set.instMembership","Set.instSProd","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.NonQuadraticHolomorphicMeanValue.0.GinibrePoincare.complex_polar_integrable","abs","abs_of_pos","congr","congrArg","congrFun'","continuous_const","continuous_id","differentiable_const","funext","id","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHMul","instHSMul","instHSub","instHasSolidNormReal","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsTopologicalAddGroupReal","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instProperSpaceReal","instSecondCountableTopologyReal","instTopologicalSpaceProd","instTransEq","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","integral_smul_const","locallyCompact_of_proper","measurableSet_Ioi","measureSpaceOfInnerProductSpace","polarCoord","polarCoord_target","rfl","smulCommClass_self","smul_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticHolomorphicMeanValue","name":"GinibrePoincare.radial_integral_holomorphic_mean_value_of_integrable","type_dependencies":["Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instDenselyNormedField","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.measurableSpace","Complex.ofReal","Continuous","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.Integrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","UniformSpace.toTopologicalSpace","instHSMul","instHSub","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoi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ormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instHDiv","instHMul","instHPow","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.PhaseRegular","GinibrePoincare.ginibreMeasure","GinibrePoincare.radial_phaseRegular_weak_mem_sobolevClosure","GinibrePoincare.radial_sobolev_lsi","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialPhaseWeakSobolevDomain","name":"GinibrePoincare.radial_phaseRegular_weak_mem_sobolevClosure","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Exists","Filter.EventuallyEq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsSymmetric","GinibrePoincare.PhaseRegular","GinibrePoincare.ginibreMeasure","GinibrePoincare.radialSobolevClosure","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.topologicalSpace","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.normedAddCommGroup","Real.semiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instFintypeProd","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","tsupport"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","Complex","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.refl","Eq.trans","EuclideanSpace","Exists","Exists.casesOn","Exists.intro","Filter.Eventually.of_forall","Filter.EventuallyEq","Filter.EventuallyEq.trans","Filter.atTop","Filter.atTop_neBot","Filter.mp_mem","Fi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iv","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.radiusBilinear","HMul.hMul","HSub.hSub","Nat","Nat.cast","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHMul","instHSub","starRingEnd"],"value_dependencies":["Complex","Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.radiusBilinear","Nat"]},{"kind":"definition","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusLeftCLM","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Fin","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.sub","DFunLike.coe","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.radiusLeftCLM._proof_1","GinibrePoincare.radiusLeftCLM._proof_2","GinibrePoincare.radiusLeftCLM._proof_3","GinibrePoincare.radiusLeftCLM._proof_4","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.instRing","Real.normedField","Real.semiring","RingHom","RingHom.id","RingHom.instFunLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instHSub","instInnerProductSpaceRealComplex","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusLeftCLM._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedField","IsTopologicalAddGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusLeftCLM._proof_2","type_dependencies":["Algebra.toSMul","Complex","Complex.instNormedField","Complex.instRCLike","Distrib.toMul","Field.toSemifield","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","SMulCommClass","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","instDistribOfSemiring","instSMulOfMul"],"value_dependencies":["Algebra.to_smulCommClass","Complex","Complex.instNormedField","Complex.instRCLike","Field.toSemifield","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","RCLike.toNormedAlgebra","Real","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusLeftCLM._proof_3","type_d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","BoundedContinuousFunction.continuous","BoundedContinuousFunction.instFunLike","BoundedContinuousFunction.instNorm","BoundedContinuousFunction.norm_coe_le_norm","CommSemiring.toSemiring","Continuous.aestronglyMeasurable","Continuous.comp","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toMul","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Equiv.Perm","Equiv.instEquivLike","Equiv.instFintype","EquivLike.toFunLike","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.univ","Fintype.card","Function.comp","GinibrePoincare.radiusPermutationAverage","HMul.hMul","InnerProductSpace.toNormedSpace","Inv.inv","LE.le","MeasurableSpace.pi","MeasureTheory.Integrable.mono'","MeasureTheory.IsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_const_mul","MeasureTheory.integral_finsetSum","Membership.mem","MetricSpace.toEMetricSpace","Nat","Nat.cast","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.instAddCommMonoid","Real.instInv","Real.instLE","Real.instMul","Real.instNatCast","Real.instRCLike","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SetLike.instMembership","UniformSpace.toTopologicalSpace","congrArg","continuous_apply","continuous_pi","id","instCountableFin","instDecidableEqFin","instDistribOfSemiring","instHMul","instSecondCountableTopologyReal","secondCountableTopologyEither_of_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialSymmetrizedLaw","name":"GinibrePoincare.radiusPermutationAverage_symmetric","type_dependencies":["Fin","GinibrePoincare.IsSymmetricRadiusTest","GinibrePoincare.radiusPermutationAverage","Nat","Real"],"value_dependencies":["DFunLike.coe","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Equiv","Equiv.Perm","Equiv.Perm.instMul","Equiv.Perm.permGroup","Equiv.instEquivLike","Equiv.instFintype","Equiv.mulLeft","Equiv.sum_comp","EquivLike.toFunLike","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.univ","Fintype.card","Function.comp","GinibrePoincare.radiusPermutationAverage","HMul","HMul.hMul","Inv.inv","Membership.mem","Nat","Nat.cast","Real","Real.instAddCommMonoid","Real.instInv","Real.instMul","Real.instNatCast","SetLike.instMembership","congr","congrArg","id","instDecidableEqFin","instHMul"]},{"kind":"definition","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusRightCLM","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Fin","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.conjCLE","Complex.instAddCommMonoid","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.sub","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.radiusLeftCLM._proof_1","GinibrePoincare.radiusLeftCLM._proof_2","GinibrePoincare.radiusLeftCLM._proof_3","GinibrePoincare.radiusLeftCLM._proof_4","GinibrePoincare.radiusRightCLM._proof_1","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.instRing","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instHSub","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusRightCLM._proof_1","type_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple","Semiring.toNonAssocSemiring"],"value_dependencies":["Real","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusRightCLM.eq_1","type_dependencies":["Complex","Complex.addCommGroup","Complex.conjCLE","Complex.instAddCommMonoid","Complex.instNatCast","Complex.instNonUnitalCommRing","Complex.instNormedField","ContinuousLinearEquiv.toContinuousLinearMap","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.comp","ContinuousLinearMap.instSMul","ContinuousLinearMap.proj","ContinuousLinearMap.sub","Eq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.coordinateSum","GinibrePoincare.coordinateSumCLM","GinibrePoincare.radiusLeftCLM._proof_1","GinibrePoincare.radiusLeftCLM._proof_2","GinibrePoincare.radiusLeftCLM._proof_3","GinibrePoincare.radiusLeftCLM._proof_4","GinibrePoincare.radiusRightCLM","GinibrePoincare.radiusRightCLM._proof_1","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.module","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.instRing","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instHSMul","instHSub","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.radiusRightCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusDifferential","name":"GinibrePoincare.radiusRightCLM_apply","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.radiusBilinear","GinibrePoincare.radiusRightCLM","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPse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","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.LinearCombination.eq_of_eq","Mathlib.Tactic.LinearCombination.eq_rearrange","Mathlib.Tactic.LinearCombination.mul_const_eq","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fderiv","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadiusGradient","name":"GinibrePoincare.radius_gradient_imaginary","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instStarRing","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.centeredScaled","GinibrePoincare.complexRadius","GinibrePoincare.imaginaryCoordinateDirection","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instHSub","instInnerProductSpaceRealComplex","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","Algebra.toModule","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.conj_I","Complex.in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inibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.realGradientNormSq","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHPow","instInnerProductSpaceRealComplex","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.realGradientNormSq","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GroundStateDbar","name":"GinibrePoincare.realGradientNormSq_centeredObservable","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.centeredObservable","GinibrePoincare.realGradientNormSq","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Eq.mpr","Eq.refl","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.centeredObservable","GinibrePoincare.fderiv_centeredObservable","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GinibrePoincare.realGradientNormSq","HAdd.hAdd","HPow.hPow","InnerProductSpace.toNormedSpace","Monoid.toNPow","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","congrArg","fderiv","id","instHAdd","instHPow","instInnerProductSpaceRealComplex","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixOverlapLowerBound","name":"GinibrePoincare.realGradientNormSq_eq_wirtinger","type_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.normSq","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.realDifferentialWirtinger","GinibrePoincare.realGradientNormSq","HMul.hMul","InnerProductSpace.toNormedSpace","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup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nCap","Min.min","NNReal","NNReal.instSemilatticeInf","Real","SemilatticeInf.toMin"],"value_dependencies":["Eq.refl","GinibrePoincare.realMartingaleHorizonCap","NNReal","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleCap","name":"GinibrePoincare.realMartingaleHorizonCap_continuous","type_dependencies":["Continuous","GinibrePoincare.realMartingaleHorizonCap","NNReal","NNReal.instTopologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Continuous","Continuous.comp","Continuous.min","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instOrderTopology","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","OrderTopology.to_orderClosedTopology","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SemilatticeInf.toMin","UniformSpace.toTopologicalSpace","continuous_const","continuous_id","id"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleCap","name":"GinibrePoincare.realMartingaleHorizonCap_eq_after","type_dependencies":["Eq","GinibrePoincare.realMartingaleHorizonCap","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Real"],"value_dependencies":["Eq","Eq.trans","GinibrePoincare.realMartingaleHorizonCap","LE.le","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","Real","SemilatticeInf.toMin","True","congrArg","congrFun'","eq_self","inf_of_le_right","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleCap","name":"GinibrePoincare.realMartingaleHorizonCap_eq_before","type_dependencies":["Eq","GinibrePoincare.realMartingaleHorizonCap","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Real"],"value_dependencies":["Eq","Eq.trans","GinibrePoincare.realMartingaleHorizonCap","LE.le","Min.min","NNReal","NNReal.instPartialOrder","NNReal.instSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","Real","SemilatticeInf.toMin","True","congrArg","congrFun'","eq_self","inf_of_le_left","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleCap","name":"GinibrePoincare.realMartingaleHorizonCap_martingale","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.realMartingaleHorizonCap","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.MemLp","NNReal","NNReal.instPartialOrder","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And.intro","And.left","And.right","Bool","Bool.true","CommSemiring.toSemiring","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","Eq","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.EventuallyEq.refl","GinibrePoincare.realMartingaleHorizonCap","Iff.mp","InnerProductSpace.toNormedSpace","LE.le","LE.le.trans","LT.lt","LT.lt.le","LinearOrder.toDecidableLE","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.mono","MeasureTheory.Filtration.seq","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsFiniteMeasure.sigmaFiniteFiltration","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable","MeasureTheory.StronglyAdapted","MeasureTheory.StronglyMeasurable.mono","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.condExp_of_stronglyMeasurable","MeasureTheory.sigmaFinite_of_sigmaFiniteFiltration","Min.min","NNReal","NNReal.instLinearOrder","NNReal.instPartialOrder","NNReal.instSemilatticeInf","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedComm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Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.measure_mono","MeasureTheory.measure_mono_ae","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","Monotone","Monotone.measure_iUnion","NNReal","NNReal.instPartialOrder","NNReal.instTopologicalSpace","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nat.instMetricSpace","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.succ_pos","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","OrderTopology.of_linearLocallyFinite","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prop.le","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instLT","Real.instMonoid","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Set","Set.Icc","Set.iInter","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra","Set.instMembership","Set.mem_iInter","Set.mem_iUnion","Set.ofPred","StarOrderedRing.toIsOrderedRing","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","Trans.trans","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.BrownianIntegralContinuousModificationMaximal.0.GinibrePoincare.realMartingale_continuous_maximal_lt_le._simp_1_1","congrArg","forall_congr","iSup","iSup_le","id","instAddNat","instArchimedeanNat","instCountableNat","instDiscreteTopologyNat","instHAdd","instHDiv","instHPow","instInhabitedNat","instIsCountablyGenerated_atTop","instIsDirectedOrder","instLENat","instNonemptyOfInhabited","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceNat","instTransLE","le_rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationMartingaleIdentification","name":"GinibrePoincare.realMartingale_difference_secondMoment_le_terminal","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.symm","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.real_condExp_square_integral_le","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Filtration.le","MeasureTheory.Filtration.seq","MeasureTheory.IsFiniteMeasure","MeasureTheory.IsFiniteMeasure.sigmaFiniteFiltration","MeasureTheory.Martingale","MeasureTheory.Martingale.condExp_ae_eq","MeasureTheory.Martingale.sub","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.sub","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.sigmaFinite_of_sigmaFiniteFiltration","Membership.mem","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.instSub","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instLE","Real.instMonoid","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","Trans.trans","UniformSpace.toTopologicalSpace","congrArg","id","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","instTransEq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticPuncturedUnitFieldPartialMeanSquare","name":"GinibrePoincare.realMartingale_eq_until_of_terminal_ae","type_dependencies":["Filter.EventuallyEq","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","NNReal","NNReal.instPartialOrder","NormedAddCommGroup.toSeminormedAddCommGroup","PartialOrder.toPreorder","Preorder.toLE","RCLike.toInnerProductSpaceReal","Real","Real.instRCLike","Real.normedAddCommGroup"],"value_dependencies":["Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.Filtration.seq","MeasureTheory.Martingale","MeasureTheory.Martingale.condExp_ae_eq","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.condExp_congr_ae","NNReal","NNReal.instPartialOrder","NormedAddCommGroup.toSeminormedAddCommGroup","PartialOrder.toPreorder","Preorder.toLE","RCLike.toInnerProductSpaceReal","Real","Real.instCompleteSpace","Real.instRCLike","Real.normedAddCommGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationSquare","name":"GinibrePoincare.realMartingale_finite_maximal_le","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instDivInvMonoid","ENNReal.instLE","ENNReal.ofNNReal","ENNReal.ofReal","Exists","HDiv.hDiv","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Set","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHDiv","instHPow","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","CommMagma.toMul","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.coe_inj._simp_1","ENNReal.coe_ne_top._simp_1","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instDivInvMonoid","ENNReal.instLE","ENNReal.instNoZeroDivisors","ENNReal.instTop","ENNReal.instZero","ENNReal.le_div_iff_mul_le","ENNReal.ofNNReal","ENNReal.ofReal","ENNReal.pow_ne_top","Eq","Eq.mpr","Eq.symm","Eq.trans","Exists","False","GinibrePoincare.realMartingale_finite_maximal_mul_le","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LT.lt.ne'","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","Or.inl","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.ofPred","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cast","congrArg","congrFun'","id","instDistribOfSemiring","instHDiv","instHMul","instHPow","instLENat","instOfNatAtLeastTwo","instOfNatNat","isReduced_of_noZeroDivisors","mul_comm","not_false_eq_true","of_eq_true","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationSquare","name":"GinibrePoincare.realMartingale_finite_maximal_mul_le","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instLE","ENNReal.ofNNReal","ENNReal.ofReal","Exists","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Set","Set.ofPred","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instHMul","instHPow","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring.toCommMonoid","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","Decidable.byContradiction","Distrib.toMul","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedMonoid","ENNReal.instLE","ENNReal.instPartialOrder","ENNReal.ofNNReal","ENNReal.ofReal","ENNReal.ofReal_le_ofReal","Eq","Eq.mp","Eq.mpr","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.le_sup'_iff","Finset.mem_range","Finset.nonempty_range_add_one","Finset.range","Finset.sup'","GinibrePoincare.realMartingale_square_submartingale","HAdd.hAdd","HMul.hMul","HPow.hPow","HasSolidNorm.orderClosedTopology","Iff","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedMonoid.toMulLeftMono","IsOrderedMonoid.toMulRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MemLp","MeasureTheory.MemLp.integrable_sq","MeasureTheory.Submartingale","MeasureTheory.ae_of_all","MeasureTh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attice","EMetricSpace.toPseudoEMetricSpace","EMetricSpace.toWeakEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENorm","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Eventually","Filter.EventuallyEq","Filter.EventuallyEq.trans","Filter.Tendsto","Filter.Tendsto.norm","Filter.Tendsto.pow","Filter.Tendsto.sub","Filter.atTop","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.actualL2Limit_eq_pathwise_subsequence_ae","GinibrePoincare.actualL2Limit_nullAugmentation_measurable","GinibrePoincare.actualMeanSquareCauchy_exists_L2_limit","GinibrePoincare.ginibreNullAugmentation","GinibrePoincare.ginibreNullAugmentation_measurable_congr","GinibrePoincare.integral_square_eq_L2_norm_sq","GinibrePoincare.realMartingale_difference_secondMoment_le_terminal","GinibrePoincare.realMartingale_memLp_two_of_le","GinibrePoincare.realMartingale_of_actual_L2_limits","GinibrePoincare.realMartingale_terminal_cauchy_exists_continuous_limit","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsTopologicalAddGroup.to_continuousSub","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LE.le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Measurable","Measurable.stronglyMeasurable","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Filtration","MeasureTheory.Filtration.seq","MeasureTheory.IsFiniteMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_sub","MeasureTheory.Lp.ext","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.memLp","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.IsComplete","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp._auto_1","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.StronglyAdapted","MeasureTheory.StronglyMeasurable.measurable","MeasureTheory.TendstoInMeasure","MeasureTheory.TendstoInMeasure.congr","MeasureTheory.ae","MeasureTheory.ae_of_all","MeasureTheory.condExp","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.integral_nonneg","MeasureTheory.memLp_congr_ae","MeasureTheory.tendstoInMeasure_of_tendsto_Lp","Membership.mem","MetricSpace.toEMetricSpace","Min.min","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.instLinearOrder","NNReal.instOrderBot","NNReal.instOrderTopology","NNReal.instPartialOrder","NNReal.instSemilatticeInf","NNReal.instTopologicalSpace","NNReal.instZero","NPow.toPow","Nat","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","OrderTopology.to_orderClosedTopology","PartialOrder.toPreorder","Pi.instSub","Preorder.toLE","Prod","Prod.fst","Prod.instPreorder","Prod.snd","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAddCommMonoid","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instPreorder","Real.instRCLike","Real.instStarOrderedRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","SemilatticeInf.toMin","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.Icc","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","StrictMono","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.mk","Subtype.val","TendstoUniformly","TendstoUniformly.tendsto_at","TopologicalSpace","True","UniformSpace.toTopologicalSpace","WeakEMetricSpace.toWeakPseudoEMetricSpace","WeakPseudoEMetricSpace.toEDist","Zero.toOfNat0","autoParam","bot_le","congr","congrArg","congrFun'","continuous_const","continuous_id","eq_of_heq","eq_self","fact_one_le_two_ennreal","funext","id","inferInstance","instClosedIciTopology","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instHasSolidNormReal","instIsOrderedModule","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSecondCountableTopologyReal","instStarRingReal","instTopologicalSpaceSubtype","min_le_right","nhds","norm_zero","of_eq_true","rfl","sq_nonneg","squeeze_zero","sub_self","tendsto_const_nhds","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationGrid","name":"GinibrePoincare.realMartingale_uniform_grid_maximal_le","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instDivInvMonoid","ENNReal.instLE","ENNReal.ofNNReal","ENNReal.ofReal","Exists","GinibrePoincare.itoUniformNNTime","HDiv.hDiv","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasurableSpace","MeasureTheory.Filtration","MeasureTheory.IsFiniteMeasure","MeasureTheory.Martingale","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Set","Set.ofPred","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHDiv","instHPow","instLENat","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring.toSemiring","ContinuousENorm.toENorm","DFunLike.coe","DistribLattice.toLattice","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instDivInvMonoid","ENNReal.instLE","ENNReal.ofNNReal","ENNReal.ofReal","Eq","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UnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","smulCommClass_self","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreBrownianIntegralPartialCauchy","name":"GinibrePoincare.real_condExp_square_integral_le","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.Measure","MeasureTheory.Measure.trim","MeasureTheory.MemLp","MeasureTheory.SigmaFinite","MeasureTheory.condExp","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.instLE","Real.instMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","Bool","Bool.true","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instIsOrderedRing","ENNReal.instOne","ENNReal.instPartialOrder","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Filter.EventuallyLE","HPow.hPow","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","Integrable.norm_condExp_rpow_le","IsScalarTower.right","LE.le","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace","MeasurableSpace.instLE","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.trim","MeasureTheory.MemLp","MeasureTheory.MemLp.condExp","MeasureTheory.MemLp.integrable_sq","MeasureTheory.SigmaFinite","MeasureTheory.ae","MeasureTheory.condExp","MeasureTheory.integrable_condExp","MeasureTheory.integral","MeasureTheory.integral_condExp","MeasureTheory.integral_mono_ae","Monoid.toNPow","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toUniformSpace","RCLike.instStarModuleReal","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.instAddGroup","Real.instCommSemiring","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instPow","Real.instRCLike","Real.instRing","Real.instStarOrderedRing","Real.lattice","Real.linearOr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.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GeneralPotentialProjectionRealVariance.0.GinibrePoincare.real_conjugation_projection_norm_sq_le_two_residual._abel_1_1","_private.GinibrePoincare.Analysis.GeneralPotentialProjectionRealVariance.0.GinibrePoincare.real_conjugation_projection_norm_sq_le_two_residual._abel_1_2","add_zero","congr","congrArg","congrFun'","eq_self","id","inferInstance","inner_add_left","inner_conj_symm","inner_sub_right","inner_zero_left","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","map_sub","map_zero","norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero","of_eq_true","pow_two","rfl","smulCommClass_self","sq_nonneg","starRingEnd","sub_self","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultDifferential","name":"GinibrePoincare.real_directional_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","ContDiff","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENat","Eq","Field.toSemifield","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instCommMonoid","Real.instRCLike","Real.instRing","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","Top.top","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","WithTop.some","fderiv","instInnerProductSpaceRealComplex","instTopENat","smulCommClass_self"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instT2Space","Complex.instZero","ContDiff","ContDiff.differentiable","ContDiff.fderiv_right","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.apply","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.module","ContinuousLinearMap.toNormedAddCommGroup","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionRing.toRing","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Function.comp","HAdd.hAdd","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Module.complexToReal","Module.toDistribMulAction","MulZero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UniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedField","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathFactorization","name":"GinibrePoincare.recenteredCLM._proof_2","type_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedField","DistribMulAction.toMulAction","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instCommMonoid","Real.instRCLike","Real.normedField","Real.semiring","SMulCommClass","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMonoid.toAddMonoid","CommMonoid.toMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedField","DistribMulAction.toMulAction","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.instCommMonoid","Real.instRCLike","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathFactorization","name":"GinibrePoincare.recenteredCLM._proof_3","type_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instRCLike","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformContinuousConstSMul.instContinuousConstSMul","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathFactorization","name":"GinibrePoincare.recenteredCLM.eq_1","type_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.instSMul","ContinuousLinearMap.pi","ContinuousLinearMap.proj","ContinuousLinearMap.sub","DistribMulAction.toDistribSMul","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.coordinateSumCLM","GinibrePoincare.recenteredCLM","GinibrePoincare.recenteredCLM._proof_1","GinibrePoincare.recenteredCLM._proof_2","GinibrePoincare.recenteredCLM._proof_3","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","Nat","Nat.cast","NonUnitalSeminormedC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Poincare.recenteredQuarterTurn.eq_1","type_dependencies":["Complex","Complex.I","Complex.instAddCommMonoid","Complex.instMul","Complex.instSemiring","Eq","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.recenteredQuarterTurn","GinibrePoincare.recenteredQuarterTurn._proof_1","GinibrePoincare.zeroSumHyperplane","HSMul.hSMul","Membership.mem","Nat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.smul","Subtype","instHSMul","instSMulOfMul"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.recenteredQuarterTurn","GinibrePoincare.zeroSumHyperplane","Membership.mem","Nat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype"]},{"kind":"definition","module":"GinibrePoincare.Analysis.EquilibriumFactorization","name":"GinibrePoincare.recenteredSqNorm","type_dependencies":["GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.recenteredConfiguration","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumFactorization","name":"GinibrePoincare.recenteredSqNorm.eq_1","type_dependencies":["Eq","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.recenteredConfiguration","GinibrePoincare.recenteredSqNorm","Nat","Real"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","GinibrePoincare.recenteredSqNorm","Nat","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.recenteredVolume","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.zeroSumHyperplane","MeasurableSpace.pi","MeasureTheory.Measure","Membership.mem","Nat","Pi.Function.module","Pi.addCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.instMeasurableSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.recenteredVolume._proof_1","GinibrePoincare.recenteredVolume._proof_2","GinibrePoincare.recenteredVolume._proof_3","GinibrePoincare.zeroSumHyperplane","MeasurableSpace.pi","MeasureTheory.Measure.addHaar","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.setLike","Subtype","Subtype.instMeasurableSpace","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.recenteredVolume._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Fin","GinibrePoincare.Configuration","GinibrePoincare.zeroSumHyperplane","IsTopologicalAddGroup","Membership.mem","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Fin","GinibrePoincare.Configuration","GinibrePoincare.zeroSumHyperplane","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.Function.module","Pi.addCommGroup","Pi.isTopologicalAddGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Submodule.isTopologicalAddGroup","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EquilibriumProbability","name":"GinibrePoincare.recenteredVolume._proof_2","type_depende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ign","GinibrePoincare.permuteConfigurationPolynomial","HMul.hMul","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.rename","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","OfNat.ofNat","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0","instDecidableEqFin","instHMul","instMulZeroClassOfSemiring"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddMonoid.toAddZeroClass","AddMonoidAlgebra.addCommGroup","AddMonoidAlgebra.algebra","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instIsTorsionFree","AddMonoidAlgebra.instModule","AddMonoidAlgebra.instMul","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.nonUnitalNonAssocRing","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","AddMonoidAlgebra.zero","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","AlgHom","AlgHom.algHomClass","AlgHom.funLike","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","Algebra.id","Algebra.toModule","Algebra.toSMul","Bool","Bool.false","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instCharZero","Complex.instCommSemiring","Complex.instField","Complex.instIntCast","Complex.instNatCast","Complex.instRing","Complex.instSemiring","DFunLike.coe","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Equiv.Perm","Equiv.Perm.permGroup","Equiv.Perm.sign","Equiv.Perm.sign_swap'","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_left","Equiv.swap_apply_of_ne_of_ne","Equiv.swap_apply_right","EquivLike.toFunLike","False","Field.toSemifield","Fin","Fin.fintype","Finsupp","Finsupp.instAdd","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.instZero","Function.comp","GinibrePoincare.ConfigurationPolynomial","GinibrePoincare.identifyVariable","GinibrePoincare.permutationSign","GinibrePoincare.permuteConfigurationPolynomial","Group.toDivInvMonoid","GroupWithZero.toNoZeroSMulDivisors","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasDistribNeg.toInvolutiveNeg","Iff.mp","Iff.mpr","Int","Int.cast","Int.cast_neg","Int.cast_one","Int.instCommRing","Int.instMonoid","InvolutiveNeg.toNeg","IsDomain.toIsCancelMulZero","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidHom","MonoidHom.id","MonoidHom.instFunLike","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MvPolynomial","MvPolynomial.C","MvPolynomial.C_neg","MvPolynomial.rename","MvPolynomial.rename_rename","Nat","Nat.cast_zero","Nat.instAddMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instMulZeroClass","Nat.instNeZeroSucc","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","One.toOfNat1","Or","Or.resolve_left","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubNegZeroMonoid.toSubNegMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Units","Units.instMulOneClass","Units.instNeg","Units.instOne","Units.val","Zero.toOfNat0","add_eq_zero_iff_eq_neg","congr","congrArg","congrFun'","dite","eq_false","eq_self","funext","id","instDecidableEqFin","instHAdd","instHMul","instHSMul","instIsDomain","instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","ite","ite_congr","ite_eq_left_of_eq_true","ite_eq_right_of_eq_false","map_neg","neg_mul","of_eq_true","one_mul","outParam","smul_eq_zero","two_smul"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerCFC","name":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ommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerCFC","name":"GinibrePoincare.resolventBackwardEuler._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerCFC","name":"GinibrePoincare.resolventBackwardEuler._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerCFC","name":"GinibrePoincare.resolventBackwardEuler._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.complexToReal","CompleteSpace","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousFunctionalCalculus","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","GinibrePoincare.resolventBackwardEuler._proof_1","GinibrePoincare.resolventBackwardEuler._proof_2","GinibrePoincare.resolventBackwardEuler._proof_6","GinibrePoincare.resolventBackwardEuler._proof_7","GinibrePoincare.resolventBackwardEuler._proof_8","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAd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logicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.instMul","ContinuousLinearMap.instSMul","ContinuousLinearMap.one","ContinuousLinearMap.sub","DistribMulAction.toDistribSMul","GinibrePoincare.resolventCfcDifferenceQuotient._proof_1","GinibrePoincare.resolventCfcDifferenceQuotient._proof_2","GinibrePoincare.resolventCfcDifferenceQuotient._proof_3","GinibrePoincare.resolventCfcEvolution","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instInv","Real.instMonoid","Real.normedField","Real.semiring","Real.toNNReal","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instHMul","instHSMul","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","Real","Real.instCommSemiring","Real.normedField","SMulCommClass","SMulZeroClass.toSMul","Semiring.toMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient._proof_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instMonoid","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient._proof_3","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","GinibrePoincare.resolventCfcDifferenceQuotient","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","Eq.rec","Eq.refl","GinibrePoincare.resolventCfcDifferenceQuotient","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.instMul","ContinuousLinearMap.instSMul","ContinuousLinearMap.one","ContinuousLinearMap.sub","DistribMulAction.toDistribSMul","Eq","GinibrePoincare.resolventCfcDifferenceQuotient","GinibrePoincare.resolventCfcDifferenceQuotient._proof_1","GinibrePoincare.resolventCfcDifferenceQuotient._proof_2","GinibrePoincare.resolventCfcDifferenceQuotient._proof_3","GinibrePoincare.resolventCfcEvolution","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instInv","Real.instMonoid","Real.normedField","Real.semiring","Real.toNNReal","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instHMul","instHSMul","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq.refl","GinibrePoincare.resolventCfcDifferenceQuotient","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient_norm_le","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.resolventCfcDifferenceQuotient","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","LE.le","LT.lt","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instLE","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instMul","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","ContinuousLinearMap.toNormedSpace","ContinuousLinearMap.toSeminormedAddCommGroup","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","Eq","Eq.mp","Eq.mpr","Field.toSemifield","GinibrePoincare.resolventCfcDifferenceQuotient","GinibrePoincare.resolventCfcDifferenceQuotient._proof_1","GinibrePoincare.resolventCfcDifferenceQuotient._proof_2","GinibrePoincare.resolventCfcDifferenceQuotient._proof_3","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventCfcEvolution_range_error_norm_le","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsBoundedSMul.continuousSMul","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","LT.lt.ne'","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal.toReal","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PolynormableSpace.continuousSMul","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.coe_toNNReal","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.isScalarTower","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Real.toNNReal","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.t2Space_of_metrizableSpace","Trans.trans","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_pos","congrArg","id","instCommCStarAlgebraComplex","instHMul","instHSMul","instHSub","instMulZeroClassOfSemiring","instPolynormableSpace","instTransEq_1","inv_mul_cancel\u2080","inv_nonneg","inv_pos","mul_le_mul_of_nonneg_left","norm_smul","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcDifferenceQuotient_range_error","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","DFunLike.coe","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.resolventCfcDifferenceQuotient","HMul.hMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","LE.le","LT.lt","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHMul","instHSub","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Bool","Bool.true","CommCStarAlgebra.toNormedCommRing","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsMulApplyEqCompId","ContinuousLinearMap.instIsOneApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instIsSubApply","ContinuousLinearMap.instMul","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","DFunLike.coe","Decidable.decide","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.resolventCfcDifferenceQuotient","GinibrePoincare.resolventCfcDifferenceQuotient._proof_1","GinibrePoincare.resolventCfcDifferenceQuotient._proof_2"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ike","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","DFunLike.coe","DenseRange","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","Filter.Tendsto","GinibrePoincare.resolventCfcDifferenceQuotient","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.Ioi","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHSub","nhds","nhdsWithin","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","Bool","Bool.false","CommCStarAlgebra.toNormedCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instStarId","ContinuousLinearMap.le_opNorm","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","ContinuousLinearMap.toSeminormedAddCommGroup","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenseRange","DenseRange.exists_dist_lt","DenselyNormedField.toNontriviallyNormedField","Dist.dist","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter.Eventually","Filter.Eventually.filter_mono","Filter.Tendsto","Filter.mp_mem","Filter.univ_mem'","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GT.gt","GinibrePoincare.resolventCfcDifferenceQuotient","GinibrePoincare.resolventCfcDifferenceQuotient_norm_le","GinibrePoincare.resolventCfcDifferenceQuotient_range_error","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mp","Iff.mpr","InnerProductSpace","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.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AddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.complexToReal","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulCommClass","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.complexToReal","CompleteSpace","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousFunctionalCalculus","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","GinibrePoincare.resolventCfcEvolution._proof_1","GinibrePoincare.resolventCfcEvolution._proof_2","GinibrePoincare.resolventCfcEvolution._proof_6","GinibrePoincare.resolventCfcEvolution._proof_7","GinibrePoincare.resolventCfcEvolution._proof_8","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.metricSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","instContinuousStarReal","instSMulOfMul","instStarRingReal"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toDivisionRing","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsSelfAdjoint.instContinuousFunctionalCalculus","IsStarNormal","IsStarNormal.instIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instSMulOfMul","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","GinibrePoincare.resolventCfcEvolution","InnerProductSpace","InnerProductSpace.toNormedSpace","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","Eq.rec","Eq.refl","GinibrePoincare.resolventCfcEvolution","InnerProductSpace","InnerProductSpace.toNormedSpace","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution_add","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.instMul","Distrib.toAdd","Eq","GinibrePoincare.resolventCfcEvolution","HAdd.hAdd","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","NNReal","NNReal.instSemiring","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instDistribOfSemiring","instHAdd","instHMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Continuous.continuousOn","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instMul","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","Distrib.toAdd","Eq","Eq.mpr","Field.toSemifield","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventCfcEvolution._proof_1","GinibrePoincare.resolventCfcEvolution._proof_2","GinibrePoincare.resolventCfcEvolution._proof_3","GinibrePoincare.resolventCfcEvolution._proof_4","GinibrePoincare.resolventCfcEvolution._proof_5","GinibrePoincare.resolventCfcEvolution._proof_9","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_add","GinibrePoincare.resolventEvolutionMultiplier_continuous","HAdd.hAdd","HMul.hMul","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NNReal","NNReal.coe_nonneg","NNReal.instSemiring","NNReal.toReal","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instMul","Real.metricSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","cfc","cfc_mul","congrArg","funext","id","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHAdd","instHMul","instStarRingReal","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcEvolution_commutes","type_dependencies":["AddCommGroup.toAddCommMonoid","Commute","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.instMul","ContinuousLinearMap.instStarId","GinibrePoincare.resolventCfcEvolution","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSelfAdjoint","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Commute","CompleteSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarId","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq.mp","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.resolventEvolutionMultiplier","InnerProductSpace"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iring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instOne","Real.instPreorder","Real.instStarOrderedRing","Real.instZero","Real.metricSpace","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cfc_nonneg","instCommCStarAlgebraComplex","instContinuousSqrtReal","instContinuousStarReal","instStarRingReal","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupCFC","name":"GinibrePoincare.resolventCfcEvolution_norm_le","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.ring","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.resolventCfcEvolution","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","LE.le","Membership.mem","Module.toDistribMulAction","NNReal","NegZeroClass.toZero","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instLE","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","And.left","And.right","Bool","Bool.true","CStarAlgebra.toNormedAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Field.toSemifield","GinibrePoincare.resolventCfcEvolution._proof_1","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_mem_unit_interval","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsOrderedAddMonoid.toAddLeftMono","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsSelfAdjoint.instIsometricContinuousFunctionalCalculus","LE.le","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.coe_nonneg","NNReal.toReal","Nat.cast_one","Nat.cast_zero","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.complexToReal","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNorm","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs_of_nonneg","congrArg","congrFun'","id","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","norm_cfc_le","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcEvolution_preserves_generator_graph","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","DFunLike.coe","Function.Injective","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventGenerator","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSelfAdjoint","LinearPMap.graph","Membership.mem","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","Commute.eq","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousLinearMap.instMul","ContinuousLinearMap.instStarId","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Function.Injective","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventCfcEvolution_commutes","GinibrePoincare.resolventGenerator","GinibrePoincare.resolventGeneratorGraph","GinibrePoincare.resolventGenerator_graph","HMul.hMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsSelfAdjoint","LinearPMap.graph","Membership.mem","Module.toDistribMulAction","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","UniformSpace.toTopologica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CommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarAlgebra.toNormedAlgebra","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","Continuous.continuousOn","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.instMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.sub","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","ContinuousOn","ContinuousOn.sub","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_continuous","GinibrePoincare.resolventEvolutionMultiplier_range_error","HMul.hMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsSelfAdjoint.instContinuousFunctionalCalculus","IsSelfAdjoint.instIsometricContinuousFunctionalCalculus","IsStarNormal","IsStarNormal.instIsometricContinuousFunctionalCalculus","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus","LE.le","Membership.mem","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","NNReal","NNReal.coe_nonneg","NNReal.toReal","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.complexToReal","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddGroup","Real.instCommSemiring","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instSub","Real.instZero","Real.metricSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","cfc","cfc_const_one","cfc_id'","cfc_mul","cfc_sub","congrArg","continuousOn_const","continuousOn_id","id","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instSMulOfMul","instStarRingReal","instTransEq","norm_cfc_le","smulCommClass_self","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcEvolution_second_error","type_dependencies":["Ad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","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.toNNReal","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcOrbit.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","GinibrePoincare.resolventCfcOrbit","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq","Eq.rec","Eq.refl","GinibrePoincare.resolventCfcOrbit","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcOrbit.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventCfcOrbit","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.toNNReal","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","Eq.refl","GinibrePoincare.resolventCfcOrbit","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventCfcOrbit_continuous","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Continuous","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DFunLike.coe","DenseRange","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.resolventCfcOrbit","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Continuous.comp","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DFunLike.coe","DenseRange","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.continuous_resolventCfcEvolution","GinibrePoincare.resolventCfcEvolution","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","Membership.mem","Module.toDistribMulAction","NNReal","NNReal.instTopologicalSpace","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","continuous_real_toNNReal","instCommCStarAlgebraComplex","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupDifferentiability","name":"GinibrePoincare.resolventCfcOrbit_hasDerivAt_range","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DFunLike.coe","DenseRange","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","GinibrePoincare.resolventCfcEvolution","GinibrePoincare.resolventCfcOrbit","HSub.hSub","HasDerivAt","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","LT.lt","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousCons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mmRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.metricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsTopologicalRing.toIsTopologicalSemiring","MetricSpace.toPseudoMetricSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.metricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","Real","Real.instCommSemiring","Real.normedField","SMulCommClass","SMulZeroClass.toSMul","Semiring.toMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.complexToReal","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulCommClass","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","name":"GinibrePoincare.resolventCfcSmoothingPreimage._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.complexToReal","CompleteSpace","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousFunctionalCalculus","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","GinibrePoincare.resolventCfcSmoothingPreimage._proof_1","GinibrePoincare.resolventCfcSmoothingPreimage._proof_2","GinibrePoincare.resolventCfcSmoothingPreimage._proof_6","GinibrePoincare.resolventCfcSmoothingPreimage._proof_7","GinibrePoincare.resolventCfcSmoothingPreimage._proof_8","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.metricSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","instContinuousStarReal","instSMulOfMul","instStarRingReal"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toDivisionRing","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsSelfAdjoint.instContinuousFunctionalCalculus","IsStarNormal","IsStarNormal.instIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instSMulOfMul","smulCommClass_self"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier","type_dependencies":["Nat","Real"],"value_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.backwardEulerResolventMultiplier","HDiv.hDiv","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instMonoid","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","instHDiv","instHPow","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier.eq_1","type_dependencies":["DivInvMonoid.toDiv","Eq","GinibrePoincare.backwardEulerResolventMultiplier","GinibrePoincare.resolventEulerMultiplier","HDiv.hDiv","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instMonoid","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instMonoid","Real.instNatCast","instHDiv","instHPow","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.resolventEulerMultiplier","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier_antitone","type_dependencies":["Antitone","GinibrePoincare.resolventEulerMultiplier","LT.lt","Membership.mem","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","Real","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Icc","Set.instMembership","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","And","And.left","And.right","Antitone","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.trans","False","Field.toSemifield","GinibrePoincare.backwardEulerResolventMultiplier","GinibrePoincare.dyadicEulerMultiplier","GinibrePoincare.dyadicEulerMultiplier_antitone","GinibrePoincare.resolventEulerMultiplier","GinibrePoincare.resolventEulerMultiplier_eq_rate","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_pow","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPreorder","Nat.pow_eq_zero._simp_1","Ne","Ne.symm","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Real","Real.decidableEq","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instMembership","Std.le_refl._simp_1","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","congr","congrArg","congrFun'","dite","false_and","funext","id","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNatPowNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat","instReflLe","lt_of_le_of_ne","mul_nonneg","mul_one","not_false_eq_true","of_eq_true","one_le_inv\u2080","sub_nonneg","sub_zero","zero_add","zero_div","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier_continuousOn","type_dependencies":["ContinuousOn","GinibrePoincare.resolventEulerMultiplier","LT.lt","Nat","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set.Icc","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","CommRing.toNonUnitalCommRing","ContinuousOn.pow","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq.refl","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.backwardEulerResolventMultiplier","GinibrePoincare.backwardEulerResolventMultiplier_continuousOn","HDiv.hDiv","HPow.hPow","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","LT.lt","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_pos'","Nat.instAddMonoidWithOne","Nat.instCommSemiring","Nat.instIsStrictOrderedRing","Nat.instMonoid","Nat.instNontrivial","Nat.instPartialOrder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","NeZero.charZero_one","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toMonoidWithZero","Set.Icc","StarOrderedRing.toIsOrderedRing","UniformSpace.toTopologicalSpace","Zero.toOfNat0","div_pos","inferInstance","instHDiv","instHPow","instIsTopologicalRingReal","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","pow_pos"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier_eq_rate","type_dependencies":["Eq","GinibrePoincare.dyadicEulerMultiplier","GinibrePoincare.resolventEulerMultiplier","HMul.hMul","HSub.hSub","Inv.inv","LT.lt","Nat","OfNat.ofNat","One.toOfNat1","Real","Real.instInv","Real.instLT","Real.instMul","Real.instOne","Real.instSub","Real.instZero","Zero.toOfNat0","instHMul","instHSub"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toSemiring","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.backwardEulerResolventMultiplier","GinibrePoincare.dyadicEulerMultiplier","GinibrePoincare.resolventEulerMultiplier","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow","HPow.hPow","HSub.hSub","Int","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LT.lt","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_div_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mo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d","zero_div","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"GinibrePoincare.resolventEulerMultiplier_tendstoUniformlyOn","type_dependencies":["Filter.atTop","GinibrePoincare.resolventEulerMultiplier","GinibrePoincare.resolventEvolutionMultiplier","LT.lt","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","Set.Icc","TendstoUniformlyOn","Zero.toOfNat0"],"value_dependencies":["Antitone.tendstoUniformlyOn_of_forall_tendsto","CompactIccSpace.isCompact_Icc","ConditionallyCompleteLinearOrder.toCompactIccSpace","Continuous.continuousOn","GinibrePoincare.resolventEulerMultiplier","GinibrePoincare.resolventEulerMultiplier_antitone","GinibrePoincare.resolventEulerMultiplier_continuousOn","GinibrePoincare.resolventEulerMultiplier_tendsto","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_continuous","LT.lt","Membership.mem","Nat","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.instConditionallyCompleteLinearOrder","Real.instIsOrderedAddMonoid","Real.instLT","Real.instOne","Real.instPreorder","Real.instZero","Real.lattice","Real.normedAddCommGroup","Real.pseudoMetricSpace","Set","Set.Icc","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHasSolidNormReal","instOrderTopologyReal"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier","type_dependencies":["Real"],"value_dependencies":["DivInvMonoid.toDiv","Eq","HDiv.hDiv","HMul.hMul","OfNat.ofNat","One.toOfNat1","Real","Real.decidableEq","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instOne","Real.instZero","Zero.toOfNat0","expNegInvGlue","instHDiv","instHMul","ite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier.eq_1","type_dependencies":["DivInvMonoid.toDiv","Eq","GinibrePoincare.resolventEvolutionMultiplier","HDiv.hDiv","HMul.hMul","OfNat.ofNat","One.toOfNat1","Real","Real.decidableEq","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instOne","Real.instZero","Zero.toOfNat0","expNegInvGlue","instHDiv","instHMul","ite"],"value_dependencies":["Eq.refl","GinibrePoincare.resolventEvolutionMultiplier","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_add","type_dependencies":["Eq","GinibrePoincare.resolventEvolutionMultiplier","HAdd.hAdd","HMul.hMul","LE.le","OfNat.ofNat","Real","Real.instAdd","Real.instLE","Real.instMul","Real.instZero","Zero.toOfNat0","instHAdd","instHMul"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.addLeftReflectLE_of_addLeftMono","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_nonpositive","GinibrePoincare.resolventEvolutionMultiplier_positive_formula","GinibrePoincare.resolventEvolutionMultiplier_zero","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","LE.le","LT.lt","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast_one","Nat.instCommSemiring","Nat.rawCast","Ne.symm","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.decidableEq","Real.decidableLT","Real.exp","Real.exp_add","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","add_pos","add_zero","congr","congrArg","congrFun'","dite","eq_self","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","le_of_not_gt","lt_of_le_of_ne","mul_one","of_eq_true","one_mul","rfl","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEigenvectors","name":"GinibrePoincare.resolventEvolutionMultiplier_contDiff","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.resolventEvolutionMultiplier","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Top.top","WithTop.some","instTopENat"],"value_dependencies":["ContDiff","ContDiff.comp","ContDiff.div_const","ContDiff.mul","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq","Eq.mpr","GinibrePoincare.resolventEvolutionMultiplier","HDiv.hDiv","HMul.hMul","InnerProductSpace.toNormedSpace","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","Not","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.decidableEq","Real.denselyNormedField","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","SeminormedCommRing.toSeminormedRing","Top.top","WithTop.some","Zero.toOfNat0","congrArg","contDiff_const","contDiff_id","dite","expNegInvGlue","expNegInvGlue.contDiff","funext","id","instHDiv","instHMul","instTopENat","ite","ite_eq_left","ite_eq_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_continuous","type_dependencies":["Continuous","GinibrePoincare.resolventEvolutionMultiplier","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","ContDiff.continuous","Continuous","Continuous.comp","Continuous.div_const","Continuous.mul","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq","Eq.mpr","GinibrePoincare.resolventEvolutionMultiplier","HDiv.hDiv","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toNormedSpace","Not","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.decidableEq","Real.denselyNormedField","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instOne","Real.instZero","Real.normedAddCommGroup","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","continuous_const","continuous_id","dite","expNegInvGlue","expNegInvGlue.contDiff","funext","id","instHDiv","instHMul","instIsTopologicalRingReal","instTopENat","ite","ite_eq_left","ite_eq_right"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_mem_unit_interval","type_dependencies":["GinibrePoincare.resolventEvolutionMultiplier","LE.le","Membership.mem","OfNat.ofNat","One.toOfNat1","Real","Real.instLE","Real.instOne","Real.instPreorder","Real.instZero","Set","Set.Icc","Set.instMembership","Zero.toOfNat0"],"value_dependencies":["AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","And","And.intro","And.left","And.right","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","Field.toSemifield","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_nonpositive","GinibrePoincare.resolventEvolutionMultiplier_positive_formula","GinibrePoincare.resolventEvolutionMultiplier_zero","GroupWithZero.toDivisionMonoid","HMul.hMul","HSub.hSub","Iff.mpr","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Membership.mem","MulZeroClass.toMul","MulZeroClass.toZero","Ne.symm","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Real","Real.decidableEq","Real.exp","Real.exp_le_one_iff","Real.exp_pos","Real.instAddCommMonoid","Real.instAddGroup","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","Set","Set.Icc","Set.instMembership","Set.mem_Icc._simp_1","Std.le_refl._simp_1","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","and_self","congr","congrArg","dite","id","instHMul","instHSub","instMulZeroClassOfSemiring","instReflLe","le_rfl","lt_of_le_of_ne","mul_nonpos_of_nonpos_of_nonneg","neg_nonpos","of_eq_true","one_le_inv\u2080","sub_nonneg","zero_le_one._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_nonpositive","type_dependencies":["Eq","GinibrePoincare.resolventEvolutionMultiplier","LE.le","LT.lt","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instZero","Zero.toOfNat0"],"value_dependencies":["DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.refl","Field.toSemifield","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier.eq_1","GroupWithZero.toDivInvMonoid","HDiv.hDiv","HMul.hMul","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","LT.lt.le","LT.lt.ne'","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.mul_zero","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","One.toOfNat1","Real","Real.decidableEq","Real.exp","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","Zero.toOfNat0","congrArg","div_nonpos_of_nonpos_of_nonneg","expNegInvGlue","expNegInvGlue.zero_of_nonpos","id","if_neg","instHDiv","instHMul","instMulZeroClassOfSemiring","ite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_positive_formula","type_dependencies":["Eq","GinibrePoincare.resolventEvolutionMultiplier","HMul.hMul","HSub.hSub","Inv.inv","LT.lt","Neg.neg","OfNat.ofNat","One.toOfNat1","Real","Real.exp","Real.instInv","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instSub","Real.instZero","Zero.toOfNat0","instHMul","instHSub"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier.eq_1","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.ne'","LinearOrder.toPartialOrder","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast_one","Nat.instCommSemiring","Nat.rawCast","NeZero.one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","Real","Real.commRing","Real.decidableEq","Real.decidableLE","Real.exp","Real.exp_add","Real.instAdd","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","congr_arg","congr_arg\u2082","div_one","div_pos","expNegInvGlue","expNegInvGlue.eq_1","id","if_neg","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsCancelMulZero","instMulZeroClassOfSemiring","instOfNat","ite","mul_neg","mul_one","ne_of_gt","neg_mul","not_le","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","name":"GinibrePoincare.resolventEvolutionMultiplier_range_error","type_dependencies":["GinibrePoincare.resolventEvolutionMultiplier","HMul.hMul","HSub.hSub","LE.le","Membership.mem","OfNat.ofNat","One.toOfNat1","Real","Real.instAddGroup","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.lattice","Set","Set.Icc","Set.instMembership","Zero.toOfNat0","abs","instHMul","instHSub"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And.left","And.right","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Decidable.decide","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.resolventEvolutionMultiplier","GinibrePoincare.resolventEvolutionMultiplier_mem_unit_interval","GinibrePoincare.resolventEvolutionMultiplier_positive_formula","GinibrePoincare.resolventEvolutionMultiplier_zero","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LE.le.trans","LT.lt","LinearOrder.toPartialOrder","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.neg_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.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ner_sub_right","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupGenerator","name":"GinibrePoincare.resolventGenerator_dense_domain","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Dense","DenseRange","Function.Injective","GinibrePoincare.resolventGenerator","InnerProductSpace","InnerProductSpace.toNormedSpace","LinearPMap.domain","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.coe","Submodule","Submodule.setLike","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Dense.mono","DenseRange","Eq","Eq.mpr","Eq.ndrec","Exists.casesOn","Function.Injective","GinibrePoincare.resolventGenerator","GinibrePoincare.resolventGeneratorGraph","GinibrePoincare.resolventGenerator_graph","GinibrePoincare.resolventGenerator_range_pair","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","LE.le","LinearPMap.domain","LinearPMap.graph","LinearPMap.mem_domain_of_mem_graph","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","Set.range","SetLike.coe","SetLike.instMembership","SubNegMonoid.toSub","Submodule","Submodule.setLike","UniformSpace.toTopologicalSpace","congrArg","id","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupGenerator","name":"GinibrePoincare.resolventGenerator_graph","type_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Eq","Function.Injective","GinibrePoincare.resolventGenerator","GinibrePoincare.resolventGeneratorGraph","InnerProductSpace","InnerProductSpace.toNormedSpace","LinearPMap.graph","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Prod","Prod.instAddCommMonoid","Prod.instModule","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Function.Injective","GinibrePoincare.resolventGeneratorGraph","GinibrePoincare.resolventGeneratorGraph_singleValued","InnerProductSpace","InnerProductSpace.toNormedSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule.toLinearPMap_graph_eq","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","name":"GinibrePoincare.resolventGenerator_graph_iff_right_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.funLike","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DFunLike.coe","DenseRange","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","Function.Injective","GinibrePoincare.resolventCfcOrbit","GinibrePoincare.resolventGenerator","HasDerivWithinAt","Iff","InnerProductSpace","InnerProductSpace.toNormedSpace","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.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","Field.toSemifield","GinibrePoincare.resolventRealCfc._proof_1","GinibrePoincare.resolventRealCfc._proof_2","GinibrePoincare.resolventRealCfc._proof_3","GinibrePoincare.resolventRealCfc._proof_4","GinibrePoincare.resolventRealCfc._proof_5","GinibrePoincare.resolventRealCfc._proof_9","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.metricSpace","Real.normedField","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","cfc","instCommCStarAlgebraComplex","instContinuousStarReal","instStarRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_2","type_dependencies":["CommRing.toNonUnitalCommRing","IsTopologicalSemiring","MetricSpace.toPseudoMetricSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.metricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsTopologicalRing.toIsTopologicalSemiring","MetricSpace.toPseudoMetricSpace","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.metricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","Real","Real.instCommSemiring","Real.normedField","SMulCommClass","SMulZeroClass.toSMul","Semiring.toMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_4","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.complexToReal","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulCommClass","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_8","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","name":"GinibrePoincare.resolventRealCfc._proof_9","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","Algebra.complexToReal","CompleteSpace","Complex","Complex.instCommSemiring","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousFunctionalCalculus","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.topologicalSpace","GinibrePoincare.resolventRealCfc._proof_1","GinibrePoincare.resolventRealCfc._proof_2","GinibrePoincare.resolventRealCfc._proof_6","GinibrePoincare.resolventRealCfc._proof_7","GinibrePoincare.resolventRealCfc._proof_8","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSelfAdjoint","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.metricSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","UniformSpace.toTopologicalSpace","instContinuousStarReal","instSMulOfMul","instStarRingReal"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instStarRing","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarRingId","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","ContinuousLinearMap.topologicalSpace","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toDivisionRing","InnerProductSpace","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsSelfAdjoint.instContinuousFunctionalCalculus","IsStarNormal","IsStarNormal.instIsometricContinuousFunctionalCalculus","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus","MetricSpace.toPseudoMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instDistribOfSemiring","instSMulOfMul","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticRadialConfinement","name":"GinibrePoincare.rhoConvexPotential_axis_second_derivative","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.ofReal","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.Potential","InnerProductSpace.toNormedSpace","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instRCLike","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","deriv","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.normSq_ofReal","Complex.ofReal","Complex.ofRealCLM","ContDiff","ContDiff.comp","ContDiff.deriv'","ContDiff.differentiable","ContinuousLinearMap.contDiff","ContinuousLinearMap.toLinearMap","ConvexOn","ConvexOn.comp_linearMap","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.mpr","Eq.refl","Field.toSemifield","Function.comp","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRhoConvexPotential._proof_1","GinibrePoincare.Potential","GinibrePoincare.strongConvex_profile_second_derivative","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set.preimage","Set.univ","UniformSpace.toTopologicalSpace","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","deriv","funext","id","instAddENat","instAddMonoidWithOneENat","instCharZeroENat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instSMulOfMul","instZeroENat","pow_two"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticRadialConfinement","name":"GinibrePoincare.rhoConvexPotential_quadratic_lower_bound","type_dependencies":["Complex","Complex.instSemiring","Complex.instZero","Complex.normSq","DFunLike.coe","DivInvMonoid.toDiv","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.semiring","Zero.toOfNat0","instHAdd","instHDiv","instHMul","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","And.right","Bool","Bool.false","Bool.true","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.normSq","Complex.normSq_neg","Complex.normSq_zero","Complex.ofReal","Complex.ofReal_inv","Convex","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRhoConvexPotential._proof_1","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","InvolutiveNeg.toNeg","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat",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inibrePoincare.convexOn_radial_lift_of_planar","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.normedField","Real.partialOrder","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Set.univ","congrArg","funext","id","instHDiv","instHMul","instHPow","instHSub","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLSI","name":"GinibrePoincare.rhoConvex_radial_lsi","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.ofReal","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.radialConfinementProbabilityDensity","GinibrePoincare.squareEntropy","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","LT.lt","MeasureTheory.Integrable","MeasureTheory.Measure","MeasureTheory.Measure.withDensity","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.log","Real.measureSpace","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","deriv","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","And.left","And.right","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.instNormedAddCommGroup","Complex.ofReal","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.ofReal","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.IsRhoConvexPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.Potential","GinibrePoincare.radialConfinementProbabilityDensity","GinibrePoincare.rhoConvex_radial_gaussian_transport","GinibrePoincare.squareEntropy","GinibrePoincare.standardGaussian_transport_lsi","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.T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group","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","ContDiff","ContDiff.continuous","ContDiff.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Field.toDivisionRing","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarBergmanProjection_eq_weak_projection","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbar","GinibrePoincare.planarWeakDbarKernel_complex_smul_mem._proof_1","GinibrePoincare.planarWeakDbarProjection","GinibrePoincare.planarWeightedTestL2","GinibrePoincare.rhoSubharmonicPotential_compact_dbar_projection_gap","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.exp","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","congrArg","fact_one_le_two_ennreal","id","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.rhoSubharmonicPotential_compact_dbar_projection_gap","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","ContDiff","ContDiff.continuous","ContDiff.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","GinibrePoincare.IsRhoSubharmonicPotential","Gini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CommMonoid","Submodule.module","Subtype","TensorProduct.addCommMonoid","TensorProduct.instModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Bool","CommMonoid.toMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDenselyNormedField","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.le_opNorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.leftDistribClass","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Field.toDivisionRing","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.PlanarComplexCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.PlanarProductCompactTensor","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.l2ProductLeftOperator","GinibrePoincare.l2ProductLeftOperator_norm_le","GinibrePoincare.l2ProductRightOperator","GinibrePoincare.l2ProductRightOperator_norm_le","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarBergman_product_projection_error","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexWeightedDbarL2","GinibrePoincare.planarComplexWeightedValueL2","GinibrePoincare.planarLeftBergmanProjection","GinibrePoincare.planarProductLeft_inverse_action","GinibrePoincare.planarProductRight_inverse_action","GinibrePoincare.planarProductWeightedDbarLeft","GinibrePoincare.planarProductWeightedDbarRight","GinibrePoincare.planarProductWeightedValue","GinibrePoincare.planarRightBergmanProjection","GinibrePoincare.rhoSubharmonicPotential_exists_bounded_dbar_inverse","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedRing.toPosMulStrictMono","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans","LE.le.trans_eq","LT.lt","LinearMap","LinearMap.instFunLike","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_pos'","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero.charZero_one","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommMonoid","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.normedAddCommGroup","Real.partialOrder","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_nonneg","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","TensorProduct.addCommMonoid","TensorProduct.instModule","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","add_le_add","congrArg","congrFun'","div_pos","fact_one_le_two_ennreal","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLTNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","le_of_lt","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_add","mul_le_mul_of_nonneg_right","mul_nonneg","mul_pos","mul_pow","norm_nonneg","secondCountable_of_proper","sq_le_sq\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductCompactGraphApproximation","name":"GinibrePoincare.rhoSubharmonicPotential_product_full_compact_gap","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toDivisionRing","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.PlanarProductDbarGraphSpace","GinibrePoincare.PlanarProductDbarGraphSpace._proof_1","GinibrePoincare.PlanarProductLebesgueL2","GinibrePoincare.PlanarProductLebesgueL2._proof_1","GinibrePoincare.planarLeftBergmanProjection","GinibrePoincare.planarRightBergmanProjection","GinibrePoincare.productCompactWeightedDbarGraph","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.t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unLike","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_one","Nat.cast_pos'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero.charZero_one","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.mk","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.semiring","Real.sq_sqrt","Real.sqrt","Real.sqrt_nonneg","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.module","Submodule.orthogonal","Submodule.setLike","Subtype","True","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","congrArg","congr_arg","congr_arg\u2082","div_one","div_pos","eq_self","fact_one_le_two_ennreal","inferInstance","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsCancelMulZero","instLTNat","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","inv_nonneg","inv_pow","measureSpaceOfInnerProductSpace","mul_nonneg","mul_one","mul_pos","mul_pow","ne_of_gt","norm_nonneg","of_eq_true","one_mul","one_ne_zero","rfl","sq_le_sq\u2080"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"GinibrePoincare.rhoSubharmonicPotential_weak_dbar_projection_gap","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContDiff.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarWeakDbarProjection","GinibrePoincare.planarWeightedAdjointTestL2","GinibrePoincare.planarWeightedTestL2","GinibrePoincare.rhoSubharmonicPotential_testL2_coercivity._proof_1","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.addCommMonoid","Submodule.module","Subtype","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","fact_one_le_two_ennreal","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","ClosedSubmodule","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContDiff.of_le","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DivisionRing.toRing","ENNReal","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ormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Top.top","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","WithTop.one","Zero.toOfNat0","instAddNat","instHAdd","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instOneENat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Bool","Bool.true","ClosedSubmodule","ClosedSubmodule.instSetLike","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContDiff.continuous","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","ENNReal.instTop","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.IsRhoSubharmonicPotential","GinibrePoincare.IsRotationalPotential","GinibrePoincare.IsSymmetric","GinibrePoincare.Potential","GinibrePoincare.potentialCenteredL2","GinibrePoincare.potentialGradientEnergy","GinibrePoincare.potentialHolomorphicQuotientProjection","GinibrePoincare.potentialHolomorphicQuotientProjection_centered_compact_gap","GinibrePoincare.potentialHolomorphicQuotient_centered_mem_positive","GinibrePoincare.potentialMeasure","GinibrePoincare.potentialPartition","GinibrePoincare.potentialPositivePhaseClosedSpan","GinibrePoincare.potentialSmoothCompact_memLp","GinibrePoincare.potentialVariance","GinibrePoincare.potentialVariance_le_two_quotient_residual_of_positive","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsOrderedRing.toPosMulMono","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNRat.rawCast"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ommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","deriv","fderiv","id","instIsRCLikeNormedField","instPolynormableSpace","lipschitzWith_of_nnnorm_fderiv_le","norm_deriv_eq_norm_fderiv"]},{"kind":"definition","module":"GinibrePoincare.Analysis.RadialGradientTransfer","name":"GinibrePoincare.scaledSquaredRadii","type_dependencies":["Fin","GinibrePoincare.Configuration","Nat","Real"],"value_dependencies":["Fin","GinibrePoincare.Configuration","GinibrePoincare.kostlanSquaredRadius","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialMagnitudeProfile","name":"GinibrePoincare.scaledSquaredRadii.eq_1","type_dependencies":["Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.kostlanSquaredRadius","GinibrePoincare.scaledSquaredRadii","Nat","Real"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.Configuration","GinibrePoincare.scaledSquaredRadii","Nat","Real"]},{"kind":"definition","module":"GinibrePoincare.Analysis.BrownianOrthogonalGaussianLaw","name":"GinibrePoincare.scaledStandardGaussian","type_dependencies":["FiniteDimensional","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","FiniteDimensional","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure.map","Module.toDistribMulAction","NNReal","NNReal.toReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","ProbabilityTheory.stdGaussian","Real","Real.instDivisionRing","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","Real.sqrt","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalGaussianLaw","name":"GinibrePoincare.scaledStandardGaussian_isProbability","type_dependencies":["FiniteDimensional","GinibrePoincare.scaledStandardGaussian","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","FiniteDimensional","GinibrePoincare.scaledStandardGaussian","HSMul.hSMul","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure.map","MeasureTheory.instIsProbabilityMeasureMap","Module.toDistribMulAction","NNReal","NNReal.toReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","ProbabilityTheory.isProbabilityMeasure_stdGaussian","ProbabilityTheory.stdGaussian","Real","Real.instDivisionRing","Real.instMonoid","Real.instRCLike","Real.normedField","Real.semiring","Real.sqrt","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","id","inferInstance","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianOrthogonalGaussianLaw","name":"GinibrePoincare.scaledStandardGaussian_measurePreserving","type_dependencies":["BorelSpace","DFunLike.coe","EquivLike.toFunLike","FiniteDimensional","GinibrePoincare.scaledStandardGaussian","InnerProductSpace","InnerProductSpace.toNormedSpace","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","MeasurableSpace","MeasureTheory.MeasurePreserving","NNReal","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","RingHomInvPair.ids","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","BorelSpace","BorelSpace.opensMeasurable","Continuous.measurable","ContinuousSMul.toMeasurableSMul","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.refl","Eq.sym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edRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDecidableEqFin","instHAdd","instTopologicalSpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurChartDerivative","name":"GinibrePoincare.schurAmbientChart._proof_1","type_dependencies":["Complex","Complex.instNonUnitalCommRing","Complex.instNormedField","Fin","Fin.fintype","IsTopologicalRing","Matrix","Matrix.nonUnitalNonAssocRing","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instTopologicalSpaceMatrix"],"value_dependencies":["Complex","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedField","Field.toDivisionRing","Fin","Fin.fintype","IsTopologicalDivisionRing.toIsTopologicalRing","Matrix.topologicalRing","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLocalChart","name":"GinibrePoincare.schurAmbientChart.eq_1","type_dependencies":["Complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instNormedField","Complex.instRing","Eq","Fin","Fin.fintype","GinibrePoincare.schurAmbientChart","GinibrePoincare.schurAmbientChart._proof_1","HAdd.hAdd","HMul.hMul","Matrix","Matrix.add","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instRing","Matrix.neg","Nat","Neg.neg","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.exp","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instDecidableEqFin","instHAdd","instTopologicalSpaceMatrix"],"value_dependencies":["Complex","Eq.refl","Fin","GinibrePoincare.schurAmbientChart","Matrix","Nat","Prod"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurChartDerivative","name":"GinibrePoincare.schurAmbientChart_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","Complex.instSub","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.schurAmbientChart","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Matrix","Matrix.add","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.module","Matrix.sub","Matrix.zero","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Prod","Prod.instAddCommGroup","Prod.instModule","Prod.mk","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instHAdd","instHSub","instInnerProductSpaceRealComplex","instTopologicalSpaceMatrix","instTopologicalSpaceProd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instMul","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instSub","Complex.instT2Space","Complex.instZero","ContinuousLinearMap","Con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italSemiring","Semiring.toOppositeModule","SeparatelyContinuousMul.to_continuousSMul","SeparatelyContinuousMul.to_continuousSMul_op","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_apply","add_assoc","add_comm","add_mul","add_zero","congr","congrArg","congrFun'","eq_self","fderiv","funext","hasFDerivAt_const","hasFDerivAt_exp_zero","hasFDerivAt_fst","hasFDerivAt_snd","id","instContinuousAddMatrix","instContinuousSMulMatrix","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupMatrix","instMulZeroOneClassOfSemiring","instPolynormableSpace","instSMulOfMul","instT2SpaceMatrix","instTopologicalSpaceMatrix","instTopologicalSpaceProd","mul_add","neg_apply","neg_zero","of_eq_true","one_apply_eq_self","one_mul","one_smul","smul_add","smul_apply","smul_neg","sub_eq_add_neg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurChartDerivative","name":"GinibrePoincare.schurAmbientChart_fderiv_lowerBlock","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.decLt","Fin.fintype","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurAmbientChart","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerJacobian","GinibrePoincare.schurLowerRow","GinibrePoincare.schurSkewCombination","InnerProductSpace.toNormedSpace","LT.lt","Lex","Lex.fintype","Matrix","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.module","Matrix.mulVec","Matrix.zero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","OrderDual","OrderDual.fintype","OrderDual.ofDual","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Subtype.fintype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fderiv","instFintypeProd","instInnerProductSpaceRealComplex","instLTFin","instTopologicalSpaceMatrix","instTopologicalSpaceProd","ofLex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instSub","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Eq.mpr","Eq.symm","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.decLt","Fin.fintype","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurAmbientChart","GinibrePoincare.schurAmbientChart_fderiv","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerJacobian","GinibrePoincare.schurLowerJacobian_skew_commutator","GinibrePoincare.schurLowerRow","GinibrePoincare.schurSkewCombination","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LT.lt","Lex","Lex.fintype","Matrix","Matrix.add","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.add_apply","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.module","Matrix.mulVec","Matrix.sub","Matrix.zero","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","OrderDual","OrderDual.fintype","OrderDual.ofDual","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instModule","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField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AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarModuleReal","Complex.instStarRing","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.trans","Field.toSemifield","Fin","HSMul.hSMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","Matrix","Matrix.addCommGroup","Matrix.conjTranspose","Matrix.conjTranspose_smul","Matrix.module","Matrix.smul","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.commRing","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","TrivialStar.star_trivial","True","congrArg","congrFun'","eq_self","instHSMul","instInnerProductSpaceRealComplex","instStarRingReal","instTrivialStarReal","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_10","type_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddSemigroup.toAdd","Complex","Complex.addGroupWithOne","Complex.instNonUnitalCommRing","Complex.instStarRing","Eq","Fin","HAdd.hAdd","InvolutiveStar.toStar","Matrix","Matrix.add","Matrix.conjTranspose","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","instHAdd"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","Complex","Complex.addGroupWithOne","Complex.instNonUnitalCommRing","Complex.instStarRing","Fin","Matrix.conjTranspose_add","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","StarRing.toStarAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_2","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","RingHom.id","RingHomInvPair","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","RingHomInvPair.ids","Semifield.toCommSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_3","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Complex","Complex.addCommGroup","Complex.instNormedField","ContinuousAdd","Fin","Matrix","Matrix.addCommGroup","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace","instTopologicalSpaceMatrix"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instNormedField","Fin","IsTopologicalAddGroup.toContinuousAdd","Matrix","Matrix.addCommGroup","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupMatrix","instTopologicalSpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_4","type_dependencies":["AddCommGroup.toAddComm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ix","Matrix.addGroup","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instTopologicalSpaceMatrix"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.addCommGroup","Complex.instNormedField","Fin","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalAddGroupMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_7","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousSMul","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Fin","InnerProductSpace.toNormedSpace","Matrix","Matrix.smul","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instTopologicalSpaceMatrix"],"value_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Fin","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","SemigroupAction.toSMul","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","UniformSpace.toTopologicalSpace","instContinuousSMulMatrix","instInnerProductSpaceRealComplex","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_8","type_dependencies":["Complex","Complex.instNormedField","Fin","Matrix","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","T2Space","UniformSpace.toTopologicalSpace","instTopologicalSpaceMatrix"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instT2Space","Fin","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instT2SpaceMatrix"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurConjTransposeCLM._proof_9","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DivisionRing.toRing","Field.toDivisionRing","Fin","InnerProductSpace.toNormedSpace","Matrix","Matrix.addCommMonoid","Matrix.module","Module.Finite","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DivisionRing.toRing","Field.toDivisionRing","Fin","Fin.fintype","Finite.of_fintype","InnerProductSpace.toNormedSpace","Module.Finite.matrix","Module.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ero","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.comp","ContinuousLinearMap.comp_apply","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.ext","ContinuousLinearMap.fst","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.hasStrictFDerivAt","ContinuousLinearMap.instSMul","ContinuousLinearMap.neg","ContinuousLinearMap.one","ContinuousLinearMap.snd","ContinuousLinearMap.zero","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","DifferentiableAt","DifferentiableAt.hasFDerivAt","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribMulActionSemiHomClass.toAddMonoidHomClass","DistribSMul.toSMulZeroClass","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.decLe","Fin.decLt","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurAmbientChart","GinibrePoincare.schurAmbientChart_fderiv","GinibrePoincare.schurCoordinateChart","GinibrePoincare.schurCoordinateEmbedding","GinibrePoincare.schurCoordinateEmbedding_apply","GinibrePoincare.schurCoordinateTangent","GinibrePoincare.schurCoordinateTangentCLM","GinibrePoincare.schurCoordinateTangentCLM_apply","GinibrePoincare.schurSkewCombination","GinibrePoincare.schurUpperCombination","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.differentiableAt","HasFDerivAt.unique","HasStrictFDerivAt","HasStrictFDerivAt.add","HasStrictFDerivAt.comp","HasStrictFDerivAt.hasFDerivAt","HasStrictFDerivAt.mul'","HasStrictFDerivAt.neg","InnerProductSpace.toNormedSpace","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","Lex","Lex.fintype","Matrix","Matrix.add","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.instCompleteSpace","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instRing","Matrix.linftyOpNormedAddCommGroup","Matrix.linftyOpNormedAlgebra","Matrix.linftyOpNormedRing","Matrix.linftyOpNormedSpace","Matrix.module","Matrix.neg","Matrix.sub","Matrix.topologicalRing","Matrix.zero","Module.toDistribMulAction","Monoid.toSemigroup","MonoidWithZero.toMulZeroOneClass","MulAction.toSemigroupAction","MulOpposite","MulOpposite.instMonoid","MulOpposite.instSemiring","MulOpposite.op","MulZeroClass.toMul","MulZeroOneClass.toMulZeroClass","Nat","Neg.neg","NegZeroClass.toZero","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.exp","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","OrderDual","OrderDual.fintype","OrderDual.ofDual","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.continuousAdd'","Pi.instAdd","Pi.instMul","Pi.instNeg","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PolynormableSpace.continuousSMul","Prod","Prod.continuousAdd","Prod.continuousSMul","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.instZero","Prod.mk","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomCompTriple.ids","SMulCommClass.opposite_mid","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toNonUnitalSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Semiring.toOppositeModule","SeparatelyContinuousMul.to_continuousSMul","SeparatelyContinuousMul.to_continuousSMul_op","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.fintype","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","fderiv","hasStrictFDerivAt_const","hasStrictFDerivAt_exp_zero","hasStrictFDerivAt_fst","hasStrictFDerivAt_snd","id","instContinuousAddMatrix","instContinuousSMulForall","instContinuousSMulMatrix","instDecidableEqFin","instDistribOfSemiring","instFintypeProd","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instLEFin","instLTFin","instPolynormableSpace","instT2SpaceMatrix","instTopologicalSpaceMatrix","instTopologicalSpaceProd","map_zero","neg_zero","ofLex","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLocalChart","name":"GinibrePoincare.schurCoordinateChart_zero","type_dependencies":["Complex","Complex.instZero","Eq","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurCoordinateChart","Matrix","Nat","OfNat.ofNat","Pi.instZero","Prod.instZero","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHomClass.toZeroHomClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instMul","Complex.instNeg","Complex.instNormedField","Complex.instRing","Complex.instSemiring","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.trans","Fin","Fin.fintype","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurAmbientChart._proof_1","GinibrePoincare.schurCoordinateChart","GinibrePoincare.schurCoordinateEmbedding","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","Matrix","Matrix.add","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.addZeroClass","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.instRing","Matrix.module","Matrix.neg","Matrix.semiring","Matrix.zero","Module.toDistribMulAction","MulZeroOneClass.toMulOneClass","Nat","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.exp","NormedSpace.exp.congr_simp","NormedSpace.exp_zero","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.instZero","Pi.topologicalSpace","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.instZero","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","Ring.toAddGroupWithOne","RingHom","RingHom.id","RingHom.instFunLike","SemilinearMapClass.distribMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_self","instDecidableEqFin","instHAdd","instInnerProductSpaceRealComplex","instMulZeroOneClassOfSemiring","instTopologicalSpaceMatrix","instTopologicalSpaceProd","map_zero","mul_one","neg_zero","of_eq_true","one_mul"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurCoordinateEmbedding","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","InnerProductSpace.toNormedSpace","Matrix","Matrix.addCommMonoid","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","Prod.instAddCommMonoid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iring.toNonAssocSemiring","Submodule","Submodule.instBot","Subtype.fintype","UniformSpace.toTopologicalSpace","instFintypeProd","instInnerProductSpaceRealComplex","instLEFin","instLTFin","instTopologicalSpaceMatrix","instTopologicalSpaceProd","ofLex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","And.left","Bot.bot","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.decLe","Fin.decLt","Fin.fintype","Function.Bijective","Function.Injective","Function.Surjective","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurCoordinateTangentCLM","Iff.mpr","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Lex","Lex.fintype","LinearMap","LinearMap.instFunLike","LinearMap.ker","LinearMap.ker_eq_bot","Matrix","Matrix.addCommGroup","Matrix.addCommMonoid","Matrix.linftyOpNormedAddCommGroup","Matrix.linftyOpNormedSpace","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OrderDual","OrderDual.fintype","OrderDual.ofDual","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.instAddCommGroup","Prod.instAddCommMonoid","Prod.instModule","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.instRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule","Submodule.instBot","Subtype.fintype","UniformSpace.toTopologicalSpace","instFintypeProd","instInnerProductSpaceRealComplex","instLEFin","instLTFin","instTopologicalSpaceMatrix","instTopologicalSpaceProd","ofLex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurCoordinateTangentEquiv._proof_6","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomSurjective","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","NontriviallyNormedField.toNormedField","NormedField.toField","Real","Real.denselyNormedField","Real.semiring","RingHom.id","RingHomInvPair.ids","RingHomSurjective.invPair","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","name":"GinibrePoincare.schurCoordinateTangentEquiv._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.toLinearMap","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Field.toSemifield","Fin","Fin.decLe","Fin.decLt","Fin.fintype","Function.Bijective","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurCoordinateTangentCLM","GinibrePoincare.schurCoordinateTangentEquiv._proof_6","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Lex","Lex.fintype","LinearMap.range","Matrix","Matrix.addCommMonoid","Matrix.linftyOpNormedAddCommGroup","Matrix.linftyOpNormedSpace","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OrderDual","OrderDual.fintype","OrderDual.ofDual","Pi.Function.module","Pi.addCommMonoid","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.normedAddCommGroup","Prod.normedSpace","Prod.snd","PseudoMetricSpace.toUniformSpac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rePoincare.SchurUpperIndex","GinibrePoincare.schurEntryCoordinatesInverse","GinibrePoincare.schurEntryCoordinatesInverse._proof_1","GinibrePoincare.schurEntryCoordinatesInverse._proof_2","GinibrePoincare.schurEntryCoordinatesInverse._proof_3","GinibrePoincare.schurLowerCLM","GinibrePoincare.schurLowerCLM_apply","GinibrePoincare.schurLowerCombination","GinibrePoincare.schurUpperCLM","GinibrePoincare.schurUpperCLM_apply","GinibrePoincare.schurUpperCombination","HAdd.hAdd","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.comp","LinearMap.fst","LinearMap.instFunLike","LinearMap.restrictScalars","LinearMap.snd","Matrix","Matrix.add","Matrix.addCommMonoid","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Pi.topologicalSpace","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","congr","congrArg","congrFun'","eq_self","instHAdd","instInnerProductSpaceRealComplex","instTopologicalSpaceMatrix","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurFullJacobian","name":"GinibrePoincare.schurEntryCoordinates_left_inv","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","DFunLike.coe","Eq","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurEntryCoordinates","GinibrePoincare.schurEntryCoordinatesInverse","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","Matrix","Matrix.addCommMonoid","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","Prod.instAddCommMonoid","Prod.instModule","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","instInnerProductSpaceRealComplex"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instZero","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.decLt","Fin.instLinearOrder","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurEntryCoordinates","GinibrePoincare.schurEntryCoordinatesInverse","GinibrePoincare.schurEntryCoordinatesInverse_apply","GinibrePoincare.schurLowerCombination","GinibrePoincare.schurLowerCombination_lowerEntry","GinibrePoincare.schurLowerCombination_upperEntries_zero","GinibrePoincare.schurUpperCombination","GinibrePoincare.schurUpperCombination_entry","GinibrePoincare.schurUpperCombination_lower_zero","HAdd.hAdd","InnerProductSpace.toNormedSpace","LE.le","LT.lt","Lex","LinearMap","LinearMap.instFunLike","Matrix","Matrix.add","Matrix.addCommMonoid","Matrix.add_apply","Matrix.ext","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","OrderDual","OrderDual.ofDual","OrderDual.toDual","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.mk","Prod.snd","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Subtype.mk","Zero.toOfNat0","add_zero","congrArg","dite","id","instHAdd","instInnerProductSpaceRealComplex","instLEFin","instLTFin","le_of_not_gt","ofLex","toLex","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurFullJacobian","name":"GinibrePoincare.schurEntryCoordinates_right_inv","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","DFunLike.coe","Eq","Fin","GinibrePoincare.SchurCoordinates","GinibrePoincare.SchurLowerIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurEntryCoordinates","GinibrePoincare.schurEntryCoordinatesInverse","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","Matrix","Matrix.addCommMonoid","Matrix.module","Nat","NonUnitalSeminormedCommRing.toNonUnitalSemi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rePoincare.schurLowerCol","GinibrePoincare.schurLowerCombination","GinibrePoincare.schurLowerRow","Nat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","And","And.left","And.right","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instOne","Complex.instSemiring","Complex.instZero","DFunLike.coe","DistribSMul.toSMulZeroClass","Eq","Eq.refl","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.decLt","Fin.fintype","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_congr","Finset.sum_ite_eq'","Finset.univ","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerCombination","GinibrePoincare.schurLowerIndex_ext","GinibrePoincare.schurLowerRow","HSMul.hSMul","Iff","Iff.intro","LT.lt","Lex","Lex.fintype","Matrix","Matrix.addCommMonoid","Matrix.single","Matrix.smul","Matrix.smul_single","Matrix.sum_apply","Membership.mem","MulZeroOneClass.toMulOneClass","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","Not","OfNat.ofNat","One.toOfNat1","OrderDual","OrderDual.fintype","OrderDual.instDecidableEq","OrderDual.ofDual","Prod","Prod.fst","Prod.snd","SMulZeroClass.toSMul","SetLike.instMembership","Subtype.fintype","Subtype.instDecidableEq","True","Zero.toOfNat0","and_self","congr","congrArg","congrFun'","eq_self","instDecidableAnd","instDecidableEqFin","instDecidableEqLex","instDecidableEqProd","instFintypeProd","instHSMul","instLTFin","instMulZeroOneClassOfSemiring","instSMulOfMul","ite","ite_congr","ite_eq_left_of_eq_true","mul_one","ofLex","of_eq_true","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurJacobian","name":"GinibrePoincare.schurLowerCombination_upperEntries_zero","type_dependencies":["Complex","Complex.instZero","Eq","Fin","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCombination","LE.le","Nat","OfNat.ofNat","Zero.toOfNat0","instLEFin"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Complex","Complex.instAddCommMonoid","Complex.instMul","Complex.instOne","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","False","Fin","Fin.decLt","Fin.fintype","Fin.instPartialOrder","Finset","Finset.instSetLike","Finset.sum","Finset.sum_congr","Finset.sum_eq_zero","Finset.univ","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerCombination","GinibrePoincare.schurLowerRow","HMul.hMul","HSMul.hSMul","LE.le","LT.lt","Lex","Lex.fintype","Matrix","Matrix.addCommMonoid","Matrix.single","Matrix.single_apply_of_ne","Matrix.smul","Matrix.sum_apply","Membership.mem","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Not","OfNat.ofNat","One.toOfNat1","OrderDual","OrderDual.fintype","OrderDual.ofDual","PartialOrder.toPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","Subtype.fintype","Subtype.property","Subtype.val","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.MatrixSchurJacobian.0.GinibrePoincare.schurLowerCombination_upperEntries_zero._simp_1_2","congr","congrArg","congrFun'","eq_false","eq_self","id","instDecidableEqFin","instFintypeProd","instHMul","instHSMul","instLEFin","instLTFin","instMulZeroClassOfSemiring","instSMulOfMul","not_false_eq_true","not_le_of_gt","ofLex","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurJacobian","name":"GinibrePoincare.schurLowerIndex_ext","type_dependencies":["Eq","Fin","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerRow","Nat"],"value_dependencies":["DFunLike.coe","Eq","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Fin","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerRow","LT.lt","Lex","Nat","OrderDual","OrderDual.ofDual","Prod","Prod.ext","Prod.fst","Prod.snd","Subtype.ext","Subtype.val","instLTFin","ofLex"]},{"kind":"definition","module":"GinibrePoincare.Analysis.MatrixSchurJacobian","name":"GinibrePoincare.schurLowerJacobian","type_dependencies":["Complex","Fin","GinibrePoincare.SchurLowerIndex","Matrix","Nat"],"value_dependencies":["Complex","Complex.instSub","Complex.instZero","Eq","Fin","GinibrePoincare.SchurLowerIndex","GinibrePoincare.schurLowerCol","GinibrePoincare.schurLowerRow","HSub.hSub","Matrix","Nat","OfNat.ofNat","Zero.toOfNat0","instDecidableEqFin","instHSub","ite"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurJacobian","name":"GinibrePoincar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NNReal","GinibrePoincare.SchurStrictUpperIndex","Nat"],"value_dependencies":["CommSemiring.toCommMonoid","Complex","ENNReal","ENNReal.instCommSemiring","Eq","Fin","Fin.decLe","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.SchurStrictUpperIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.complexCoordinateGaussianDensity","LE.le","Nat","Ne","Prod","Prod.fst","Prod.snd","Subtype.fintype","Subtype.val","instDecidableEqFin","instDecidableNot","instFintypeProd","instLEFin"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurUpperGaussian","name":"GinibrePoincare.schurStrictUpperGaussianDensity_formula","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","Fin","Fin.decLe","Fin.fintype","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.SchurStrictUpperIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurStrictUpperGaussianDensity","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","Nat.cast","Ne","Neg.neg","Prod","Prod.fst","Prod.snd","Real","Real.exp","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.pi","Real.semiring","Subtype.fintype","Subtype.val","instDecidableEqFin","instDecidableNot","instDistribOfSemiring","instFintypeProd","instHDiv","instHMul","instHPow","instLEFin","instMulZeroOneClassOfSemiring"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_mul","ENNReal.ofReal_prod_of_nonneg","Eq","Eq.mpr","Eq.symm","Field.toSemifield","Fin","Fin.decLe","Fin.fintype","Finset","Finset.card","Finset.card_univ","Finset.instSetLike","Finset.mul_sum","Finset.prod","Finset.prod_const","Finset.prod_mul_distrib","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.SchurStrictUpperIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.complexCoordinateGaussianDensity","GinibrePoincare.schurStrictUpperGaussianDensity","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","HPow.hPow","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt.le","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nat.cast_nonneg'","Ne","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Prod","Prod.fst","Prod.snd","Real","Real.commRing","Real.exp","Real.exp_pos","Real.exp_sum","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.pi","Real.pi_pos","Real.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","SetLike.instMembership","Subtype.fintype","Subtype.val","Zero.toOfNat0","congrArg","div_nonneg","id","instDecidableEqFin","instDecidableNot","instDistribOfSemiring","instFintypeProd","instHDiv","instHMul","instHPow","instLEFin","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","le_of_lt","mul_nonneg","pow_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSchurUpperGaussian","name":"GinibrePoincare.schurStrictUpperGaussianDensity_integral","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instOne","Eq","Fin","Fin.decLe","Fin.fintype","GinibrePoincare.SchurStrictUpperIndex","GinibrePoincare.SchurUpperIndex","GinibrePoincare.schurStrictUpperGaussianDensity","LE.le","LT.lt","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.lintegral","Nat","Ne","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.snd","Subtype.fintype","Subtype.val","instDecidableEqFin","instDecidableNot","instFintypeProd","instInnerProd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ormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom","RingHom.id","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun","congrFun'","eq_self","fderiv","fderiv_fun_const","funext","instInnerProductSpaceRealComplex","instOfNatNat","of_eq_true","starRingEnd","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SumRadiusCoordinates","name":"GinibrePoincare.second_sumRadiusCoordinate_two","type_dependencies":["Complex","Complex.instMul","Complex.instNatCast","Eq","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.complexRadius","GinibrePoincare.complexSecondDirectionalDerivative","GinibrePoincare.sumRadiusCoordinate","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.second_complexRadius","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SumRadiusCoordinates","name":"GinibrePoincare.second_sumRadiusCoordinate_zero","type_dependencies":["Complex","Complex.instZero","Eq","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.complexSecondDirectionalDerivative","GinibrePoincare.sumRadiusCoordinate","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instZero","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Eq.trans","Field.toSemifield","Fin","Fin.instOfNat","GinibrePoincare.Configuration","GinibrePoincare.complexSecondDirectionalDerivative","GinibrePoincare.coordinateSum","GinibrePoincare.fderiv_coordinateSum","GinibrePoincare.sumRadiusCoordinate","InnerProductSpace.toNormedSpace","Nat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun","congrFun'","eq_self","fderiv","fderiv_fun_const","funext","instInnerProductSpaceRealComplex","instOfNatNat","of_eq_true","zero_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticCompactConvolutionSupport","name":"GinibrePoincare.separatedCompactConvolution_eq_zero_of_not_mem","type_dependencies":["Complex","Complex.borelSpace","Complex.instAdd","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSub","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.rOut","Eq","FiniteDimensional.rclike_to_real","GinibrePoincare.separatedPlanarBump","HAdd.hAdd","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Max.max","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Metric.closedBall","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","Prod","Prod.instAdd","Prod.instMeasurableSpace","Prod.instSub","Prod.instZero","Prod.pseudoMetricSpaceMax","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instMax","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.add","Set.instMembership","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopologicalSpaceProd","measureSpaceOfInnerProductSpace","tsupport"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGr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Space","Real","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterExpansion","name":"GinibrePoincare.slaterDegreeMass_eq_mode_norm","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.slaterDegreeMass","HPow.hPow","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instMonoid","Ring.toSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","UniformSpace.toTopologicalSpace","instHPow","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Decidable.decide","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianAlternatingL2","GinibrePoincare.gaussianHermiteCoefficient","GinibrePoincare.gaussianHermiteMode","GinibrePoincare.hasSum_coefficient_norm_sq_of_totalAntiDegree","GinibrePoincare.slaterCoefficient","GinibrePoincare.slaterCoefficient_norm_sq","GinibrePoincare.slaterDegreeMass","GinibrePoincare.slaterMultiplicity","GinibrePoincare.slaterMultiplicity_pos","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HDiv.hDiv","HMul.hMul","HPow.hPow","HasSum.tsum_eq","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LT.lt.ne'","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Ta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_proof_4","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_lt._simp_1","Nat.cast_one","Nat.cast_pos'","Nat.cast_zero","Nat.factorial","Nat.factorial_pos","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.rawCast","Ne","NeZero.charZero_one","NeZero.one","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toNormSMulClass","Not","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Pi.instZero","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommMonoid","Real.instCommMonoidWithZero","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsDomain","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instStarOrderedRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_pos","Real.sqrt_pos_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Top.top","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_of_pos","addRightReflectLE_of_addLeftReflectLE","cast","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","contravariant_lt_of_covariant_le","div_one","div_pos","eq_false","eq_self","fact_one_le_two_ennreal","id","inferInstance","instAddNat","instCommCStarAlgebraComplex","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsCancelMulZero","instIsRightCancelAddOfAddRightReflectLE","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instStarRingReal","inv_mul_cancel\u2080","inv_pos","le_of_lt","mul_nonneg_of_nonpos_of_nonpos","mul_one","mul_pos","mul_pos_of_neg_of_neg","mul_right_cancel\u2080","neg_eq_zero","norm_nonneg","norm_smul","not_false_eq_true","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","pow_pos","rfl","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterPoincare","name":"GinibrePoincare.slater_centered_transform_alternating","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddS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oid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","EuclideanSpace","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Finset.range","Finset.sum","Finset.sum_singleton","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.totalAntiDegree","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullGradientL2","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.IsGinibreDistributionalGradient","GinibrePoincare.IsGinibreSymmetricWeakPair","GinibrePoincare.ginibreFullCenteredTransform","GinibrePoincare.ginibreL2Variance","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreWeakEnergy","GinibrePoincare.slaterCoefficient","GinibrePoincare.slaterDegreeMass","GinibrePoincare.slaterMultiplicity","GinibrePoincare.slaterMultiplicity_pos","GinibrePoincare.slater_ginibre_weak_energy","GinibrePoincare.slater_ginibre_weak_parseval","GinibrePoincare.slater_ginibre_zero_degree_half_mass","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasSolidNorm.orderClosedTopology","HasSum","HasSum.summable","HasSum.tsum_eq","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.natCast_nonneg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","Membership.mem","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","Mul","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PiLp.innerProductSpace._proof_1","PiLp.normedAddCommGroup","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.mk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hCompactL2._proof_1","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","ContinuousENorm.toENorm","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.coordinateMulMultivariateNormalizedL2._proof_1","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOneENat"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","BorelSpace.opensMeasurable","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","ContDiff","ContDiff.continuous","Continuous.memLp_of_hasCompactSupport","DenselyNormedField.toNontriviallyNormedField","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Fin","Fin.fintype","Finite.of_fintype","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.instIsProbabilityMeasureComplexGaussianMeasure","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure","MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MetricSpace.toEMetricSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","Pi.borelSpace","Pi.normedAddCommGroup","Pi.normedSpace","Pi.opensMeasurableSpace","Pi.topologicalSpace","PolishSpace.toSecondCountableTopology","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoEMetricSpace.toUniformSpace","PseudoMetricSpace.toPseudoEMetricSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.pseudoMetrizableSpace_pi","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instCountableFin","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instSigmaCompactSpaceForallOfFinite","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Endgame.ConcreteTheoremOneNine","name":"GinibrePoincare.smoothCompactL2.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Eq","Eq.ndrec","Fin","Fin.fintype","Ginibre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ifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","HasDerivAt.congr_of_eventuallyEq","HasDerivAt.deriv","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder.toPartialOrder","Membership.mem","NegZeroClass.toZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instIsOrderedAddMonoid","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.smoothTransition","Real.smoothTransition.one_of_one_le","Real.smoothTransition.zero_of_nonpos","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","Semiring.toModule","Set","Set.Icc","Set.instMembership","Set.ofPred","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest.0.GinibrePoincare.smoothTransition_deriv_zero_outside._simp_1_1","_private.GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest.0.GinibrePoincare.smoothTransition_deriv_zero_outside._simp_1_2","_private.GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest.0.GinibrePoincare.smoothTransition_deriv_zero_outside._simp_1_3","congr","congrArg","deriv","eventually_gt_nhds","eventually_lt_nhds","hasDerivAt_const","id","instClosedIciTopology","instClosedIicTopology","instDistribLatticeOfLinearOrder","instHasSolidNormReal","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","name":"GinibrePoincare.smooth_dbarComponent_add","type_dependencies":["Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","HAdd.hAdd","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.instAdd","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","WithTop.some","instHAdd","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.add_apply","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsAddApply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsTopologicalAddGroup.toContinuousAdd","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mat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","MeasureTheory.integral_zero","MeasureTheory.tendsto_integral_of_dominated_convergence","MetricSpace.toEMetricSpace","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.instPreorder","Nat.rawCast","Ne","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","One.toOfNat1","OrderTop.toTop","PartialOrder.toPreorder","Pi.instMul","Pi.instPow","Pi.instSub","Preorder.toLE","Preorder.toLT","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.measurableSpace","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.coe_eq_zero._simp_1","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.one","WithTop.one_ne_top._simp_2","WithTop.some","WithTop.top","WithTop.zero","Zero.toOfNat0","abs","abs_nonneg","abs_of_nonneg","addRightReflectLE_of_addLeftReflectLE","congrArg","congrFun'","contravariant_lt_of_covariant_le","deriv","div_le_iff\u2080","id","inferInstance","instAddMonoidWithOneENat","instAddNat","instCharZeroENat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instOrderTopENat","instPreorderENat","instSecondCountableTopologyReal","instTopENat","instZeroENat","le_of_not_gt","le_rfl","mul_le_mul_of_nonneg_right","mul_nonneg_of_nonpos_of_nonpos","neg_eq_zero","nhds","not_false_eq_true","of_eq_true","one_mul","rfl","secondCountableTopologyEither_of_right","sq_abs","sq_nonneg","sub_eq_zero_of_eq","sub_self","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_compact","type_dependencies":["GinibrePoincare.sobolevCutoff","HasCompactSupport","Nat","PseudoMetricSpace.toUniformSpace","Real","Real.instZero","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Bool","CommRing.toNonUnitalCommRing","ContDiffBump","ContDiffBump.hasCompactSupport","ContDiffBu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InnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instDivInvMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","deriv","div_eq_mul_inv","funext","hasDerivAt_id","id","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instMulZeroOneClassOfSemiring","instOneENat","instPolynormableSpace","instZeroENat","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_deriv_bound","type_dependencies":["And","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","Exists","Field.toSemifield","GinibrePoincare.sobolevCutoff","HAdd.hAdd","HDiv.hDiv","LE.le","Nat","Nat.cast","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instNatCast","Real.instOne","Real.instZero","Real.lattice","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","deriv","instHAdd","instHDiv"],"value_dependencies":["AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","And","And.intro","Bool","CommSemiring.toSemiring","ContDiff.continuous_deriv","ContDiffBump.contDiff","ContDiffBump.hasCompactSupport","ContDiffBump.toFun","Continuous.bounded_above_of_compact_support","DenselyNormedField.toNontriviallyNormedField","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.sobolevCutoff_deriv","HAdd.hAdd","HDiv.hDiv","HasCompactSupport.deriv","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LE.le.trans","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNormedAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAddGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Std.le_refl._simp_1","True","True.intro","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.one","WithTop.some","Zero.toOfNat0","abs","abs_div","abs_of_pos","congrArg","deriv","div_le_div_of_nonneg_right","eq_true","id","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instMulZeroClassOfSemiring","instOfNatNat","instOneENat","instPreorderENat","instReflLe","le_of_lt","norm_nonneg","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_mem_unit","type_dependencies":["And","GinibrePoincare.sobolevCutoff","LE.le","Nat","OfNat.ofNat","One.toOfNat1","Real","Real.instLE","Real.instOne","Real.instZero","Zero.toOfNat0"],"value_dependencies":["And.intro","ContDiffBump.le_one","ContDiffBump.nonneg","DivInvMonoid.toDiv","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional.rclike_to_real","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","HAdd.hAdd","HDiv.hDiv","InnerProductSpace.toNormedSpace","LE.le","Nat","Nat.cast","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Zero.toOfNat0","instHAdd","instHDiv"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_mul_tendsto","type_dependencies":["And","CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Field.toSemifield","Filter.Tendsto","Filter.atTop","GinibrePoincare.sobolevCutoff","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","Nat.instPreorder","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","deriv","instHMul","instOneENat","nhds"],"value_dependencies":["AddMonoid.toAddZeroClass","And.intro","And.left","And.right","Bool","Bool.false","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasDerivAt","Distrib.toAdd","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","False","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.mul_const","Filter.atTop","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoff_smooth","GinibrePoincare.sobolevCutoff_tendsto","HAdd.hAdd","HMul.hMul","HasDerivAt.deriv","HasDerivAt.mul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.cast_one","Nat.cast_zero","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddMonoid","Real.instMul","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.coe_eq_zero._simp_1","WithTop.one","WithTop.some","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun'","deriv","funext","id","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHAdd","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOneENat","instTopENat","instZeroENat","nhds","not_false_eq_true","of_eq_true","one_mul","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_smooth","type_dependencies":["ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.sobolevCutoff","InnerProductSpace.toNormedSpace","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Top.top","WithTop.some","instTopENat"],"value_dependencies":["ContDiff","ContDiff.comp","ContDiff.div_const","ContDiffBump.contDiff","ContDiffBump.toFun","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional.rclike_to_real","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","HAdd.hAdd","HDiv.hDiv","InnerProductSpace.toNormedSpace","Nat","Nat.cast","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instDivInvMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Top.top","WithTop.some","Zero.toOfNat0","contDiff_id","id","instHAdd","instHDiv","instTopENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevTruncation","name":"GinibrePoincare.sobolevCutoff_tendsto","type_dependencies":["And","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Filter.Tendsto","Filter.atTop","GinibrePoincare.sobolevCutoff","Nat","Nat.instPreorder","NontriviallyNormedField.toNormedField","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instOne","Real.instZero","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv","nhds"],"value_dependencies":["AddGroup.toSubtractionMonoid","And","And.casesOn","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","ContDiff.continuous","ContDiffBump.contDiff","ContDiffBump.one_of_mem_closedBall","ContDiffBump.toFun","Continuous.continuousAt","ContinuousAt.tendsto","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENat","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.casesOn","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter","Filter.Tendsto","Filter.Tendsto.comp","Filter.Tendsto.const_mul","Filter.atTop","Filter.tendsto_atTop_add_const_right","FiniteDimensional.rclike_to_real","Function.comp","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.sobolevCutoff_deriv_bound","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff.mpr","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Lattice.toSemilatticeInf","Membership.mem","Metric.closedBall","Metric.mem_closedBall._simp_1","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","Nat","Nat.cast","Nat.instPreorder","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedSpace","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instArchimedean","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","abs","congrArg","congrFun'","deriv","dist_self","div_eq_mul_inv","funext","id","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instOneENat","instOrderTopologyReal","nhds","norm_nonneg","of_eq_true","squeeze_zero","tendsto_inv_atTop_zero","tendsto_natCast_atTop_atTop","tendsto_zero_iff_norm_tendsto_zero","zero_le_one._simp_1"]},{"kind":"definition","module":"GinibrePoincare.Analysis.SobolevValueTruncation","name":"GinibrePoincare.sobolevValueTruncation","type_dependencies":["Nat","Real"],"value_dependencies":["GinibrePoincare.sobolevCutoff","HMul.hMul","Nat","Real","Real.instMul","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevValueTruncation","name":"GinibrePoincare.sobolevValueTruncation.eq_1","type_dependencies":["Eq","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevValueTruncation","HMul.hMul","Nat","Real","Real.instMul","instHMul"],"value_dependencies":["Eq.refl","GinibrePoincare.sobolevValueTruncation","Nat","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevValueTruncation","name":"GinibrePoincare.sobolevValueTruncation_bounded","type_dependencies":["GinibrePoincare.sobolevValueTruncation","HAdd.hAdd","HMul.hMul","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Norm.norm","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.norm","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","Bool","ContDiffBump.rOut","ContDiffBump.toFun","ContDiffBump.tsupport_eq","Dist.dist","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.sobolevCutoffBump._proof_3","GinibrePoincare.sobolevValueTruncation","GinibrePoincare.sobolevValueTruncation_norm_le","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Metric.closedBall","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.decidableLE","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Set","Set.instMembership","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.SobolevValueTruncation.0.GinibrePoincare.sobolevValueTruncation_bounded._simp_1_1","abs","abs_div","abs_of_pos","congrArg","congrFun'","dite","div_le_iff\u2080","id","image_eq_zero_of_notMem_tsupport","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","mul_pos","norm_zero","sub_zero","tsupport"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevValueTruncation","name":"GinibrePoincare.sobolevValueTruncation_deriv","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevValueTruncation","HAdd.hAdd","HMul.hMul","Nat","NontriviallyNormedField.toNormedField","NormedField.toField","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","deriv","instHAdd","instHMul"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","CommSemiring.toSemiring","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasDerivAt","Distrib.toAdd","Distrib.toMul","DivisionRing.toRing","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mp","Eq.trans","False","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoff_smooth","GinibrePoincare.sobolevValueTruncation","HAdd.hAdd","HMul.hMul","HasDerivAt.deriv","HasDerivAt.mul","InnerProductSpace.toNormedSpace","MulZeroOneClass.toMulOneClass","Nat","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toField","NormedRing.toRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","Pi.instMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","deriv","hasDerivAt_id","id","instDistribOfSemiring","instHAdd","instHMul","instMulZeroOneClassOfSemiring","instTopENat","instZeroENat","mul_one","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SobolevValueTruncation","name":"GinibrePoincare.sobolevValueTruncation_deriv_bound","type_dependencies":["And","CommSemiring.toSemiring","DenselyNormedField.toNontriviallyNormedField","Exists","Field.toSemifield","GinibrePoincare.sobolevValueTruncation","LE.le","Nat","NontriviallyNormedField.toNormedField","Norm.norm","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instLE","Real.instZero","Real.norm","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","Zero.toOfNat0","deriv"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.left","And.right","Bool","Bool.false","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommSemiring.toSemiring","ContDiffBump.rOut","ContDiffBump.toFun","ContDiffBump.tsupport_eq","Decidable.decide","DenselyNormedField.toNontriviallyNormedField","Dist.dist","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.sobolevCutoff","GinibrePoincare.sobolevCutoffBump","GinibrePoincare.sobolevCutoffBump._proof_3","GinibrePoincare.sobolevCutoff_deriv","GinibrePoincare.sobolevCutoff_deriv_bound","GinibrePoincare.sobolevCutoff_mem_unit","GinibrePoincare.sobolevValueTruncation","GinibrePoincare.sobolevValueTruncation_deriv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mp","InnerProductSpace.toNormedSpace","Int","Int.instDecidableEq","Int.instNegInt","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LE.le.trans","List.nil","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2081","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2082","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval\u2083","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","Metric.closedBall","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NeZero.one","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.toNormMulClass","NormedField.toField","NormedField.toNormedDivisionRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toDist","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.decidableLE","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Set","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.SobolevValueTruncation.0.GinibrePoincare.sobolevValueTruncation_deriv_bound._simp_1_8","abs","abs_div","abs_nonneg","abs_of_nonneg","abs_of_pos","add_le_add","congrArg","congrFun'","congr_arg\u2082","deriv","deriv_of_notMem_tsupport","dite","div_le_iff\u2080","div_one","eq_self","id","inferInstance","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instHSub","instIsCancelMulZero","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instTransEq_1","le_of_lt","mul_le_mul","mul_nonneg","mul_one","ne_of_gt","norm_add_le","norm_mul","norm_zero","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","rfl","sub_zero","tsupport","zero_div"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreValueTruncationChainLimits","name":"GinibrePoincare.sobolevValueTruncation_lipschitz","type_dependencies":["EMetricSpace.toPseudoEMetricSpace","Exists","GinibrePoincare.sobolevValueTruncation","LipschitzWith","MetricSpace.toEMetricSpace","NNReal","Nat","Real","Real.metricSpace"],"value_dependencies":["And","And.casesOn","CommSemiring.toSemiring","ContDiff.differentiable","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","EMetricSpace.toPseudoEMetricSpace","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Field.toSemifield","GinibrePoincare.sobolevValueTruncation","GinibrePoincare.sobolevValueTruncation_deriv_bound","GinibrePoincare.sobolevValueTruncation_smooth","InnerProductSpace.toNorm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","RingHom.id","Semiring.toModule","Semiring.toNonAssocSemiring","instLTNat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_mul","ContDiff.differentiable","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.const_mul","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","False","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Finite.of_fintype","Finset","Finset.instSetLike","Finset.instSingleton","Finset.sum","Finset.sum_apply","Finset.sum_congr","Finset.sum_singleton","Finsupp","Finsupp.apply_linearCombination","Finsupp.instAddCommMonoid","Finsupp.instFunLike","Finsupp.instZero","Finsupp.linearCombination","Finsupp.module","Finsupp.single","Finsupp.single_eq_same","Finsupp.smulZeroClass","Finsupp.support","Finsupp.support_single","Function.comp","Function.hasSMul","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteFunction","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.raiseHermiteIndex","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.contDiff_multivariateNormalized_real","GinibrePoincare.gaussianDbarAdjointTest","GinibrePoincare.spectralAdjoint_const_mul","GinibrePoincare.spectralAdjoint_finset_sum","GinibrePoincare.spectralAdjoint_hermite_ae","GinibrePoincare.spectralRaisingCoefficients","HAdd.hAdd","HMul.hMul","HSMul.hSMul","Iff.mpr","InnerProductSpace.toNormedSpace","LE.le","LT.lt","LinearMap","LinearMap.instFunLike","LinearMap.semilinearMapClass","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.ae_all_iff","Membership.mem","Module.toDistribMulAction","Monoid.toMulAction","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_add","Nat.cast_mul","Nat.cast_nonneg._simp_1","Nat.cast_one","Nat.cast_zero","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toModule","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.addCommMonoid","Pi.mulAction","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instIsOrderedRing","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instRing","Real.normedField","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_mul","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemilinearMapClass.toMulActionSemiHomClass","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Singleton.singleton","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.one","WithTop.zero","Zero.toOfNat0","congr","congrArg","congrFun","congrFun'","eq_self","funext","id","instAddMonoidWithOneENat","instAddNat","instCharZeroENat","instCountableForallOfFinite","instCountableNat","instCountableProd","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","instOneENat","instSMulOfMul","instZeroENat","map_smul","not_false_eq_true","of_eq_true","one_ne_zero._simp_1","one_smul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial","name":"GinibrePoincare.spectralAdjoint_finiteHermite_memLp","type_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Complex","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","Finsupp","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteFunction","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianDbarAdjointTest","LT.lt","MeasurableSpace.pi","MeasureTheory.MemLp","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContinuousENorm.toENorm","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.module","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.finiteHermiteCombination","GinibrePoincare.ComplexHermite.finiteHermiteCombination_coeFn","GinibrePoincare.ComplexHermite.finiteHermiteFunction","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianDbarAdjointTest","GinibrePoincare.spectralAdjoint_finiteHermite_ae","GinibrePoincare.spectralRaisingCoefficients","Iff.mp","LT.lt","LinearMap","LinearMap.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.memLp","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.ae","MeasureTheory.memLp_congr_ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype.val","UniformSpace.toTopologicalSpace","instLTNat","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial","name":"GinibrePoincare.spectralAdjoint_finset_sum","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","Finset","Finset.instSetLike","Finset.sum","GinibrePoincare.Configuration","GinibrePoincare.gaussianDbarAdjointTest","InnerProductSpace.toNormedSpace","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCo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Monoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.EventuallyEq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.spectralAntiVandermonde","HMul.hMul","InvolutiveStar.toStar","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarAlgebra.toCStarRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommMagma.toMul","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.trans","Field.toSemifield","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianMeasure_absolutelyContinuous_ginibreMeasure","GinibrePoincare.ginibreMassEvaluation","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.normalizedVandermondeL2_coeFn_public","GinibrePoincare.normalizedVandermondeMultiplier","GinibrePoincare.spectralAntiVandermonde","HMul.hMul","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_star","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instStarForall","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHomCompTriple.comp_apply","RingHomInvPair.instStarRingEnd","RingHomInvPair.triples\u2082","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarMul.toInvolutiveStar","StarRing.toStarAddMonoid","StarRing.toStarMul","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","True","UniformSpace.toTopologicalSpace","congrArg","congrFun'","eq_self","fact_one_le_two_ennreal","id","instCommCStarAlgebraComplex","instHMul","instLTNat","instOfNatAtLeastTwo","instOfNatNat","of_eq_true","starRingEnd","star_mul'"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralDifferentialFactorization","name":"GinibrePoincare.spectralBarNumber_vandermonde","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.instSub","ContDiff","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","Eq","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset.Ioi","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.dbarComponent","GinibrePoincare.spectralDifferentialBarNumber","GinibrePoincare.vandermonde","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","Nat.cast","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","RingHom","RingHom.instFunLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Top.top","WithTop.some","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","starRingEnd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instStarRing","Complex.instSub","ContDiff","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.mpr","Eq.refl","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.erase","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_add_distrib","Finset.sum_congr","Finset.sum_div","Finset.sum_neg_distrib","Finset.sum_sub_distrib","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","GinibrePoincare.dbarComponent","GinibrePoincare.spectralBarNumber_vandermonde_coordinate","GinibrePoincare.spectralCoulomb_pair_sum","GinibrePoincare.spectralDifferentialBarNumber","GinibrePoincare.vandermonde","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.cast","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NonUnitalSemiring.toSemigroupWithZero","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.denselyNormedField","Real.instRCLike","RingHom","RingHom.instFunLike","Semifield.toDivisionSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","WithTop.some","congrArg","congrFun'","eq_self","id","instDecidableEqFin","instHAdd","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat","mul_assoc","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpec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ormedAlgebra","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instLT","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instSingletonSet","Set.instUnion","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Union.union","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHSMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","smulCommClass_self","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.ofReal","Complex.ofReal_one","Complex.ofReal_sub","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.algebra","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.semiring","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.spectralSupportCFC_real_pencil_isUnit","HAdd.hAdd","HDiv.hDiv","HSMul.hSMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsTopologicalAddGroup.toContinuousAdd","IsUnit","LE.le","LT.lt","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.ofReal","RCLike.real_smul_eq_coe_smul","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instLT","Real.instMonoid","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instSingletonSet","Set.instUnion","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Union.union","Zero.toOfNat0","congrArg","id","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHSMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","smulCommClass_self","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralSupportCFC","name":"GinibrePoincare.spectralSupportCFC_pencil_isUnit_of_positive_polynomial","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommMonoid.toMonoid","CommRing.toCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.commRing","Complex.instCommSemiring","Complex.instContinuousStar","Complex.instDenselyNormedField","Complex.instField","Complex.instMul","Complex.instNonUnita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ocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedDivisionRing","NormedRing.toMetricSpace","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.commRing","Real.instAddGroup","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.instZero","Real.metricSpace","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddGroupWithOne","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","cfc","cfc_const_mul_id","cfc_const_one","cfc_id'","cfc_mul","cfc_pow","cfc_sub","congrArg","continuousOn_const","continuousOn_id'","continuous_id'","id","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousStarReal","instDistribOfSemiring","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instStarRingReal","smulCommClass_self","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralSupportCFC","name":"GinibrePoincare.spectralSupportCFC_real_pencil_isUnit","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.algebra","ContinuousLinearMap.instSMul","ContinuousLinearMap.instStarId","ContinuousLinearMap.one","ContinuousLinearMap.ring","ContinuousLinearMap.semiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","Field.toSemifield","HAdd.hAdd","HDiv.hDiv","HSMul.hSMul","HSub.hSub","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","IsTopologicalAddGroup.toContinuousAdd","IsUnit","LE.le","LT.lt","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Neg.neg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instLT","Real.instMonoid","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instSingletonSet","Set.instUnion","Singleton.singleton","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Union.union","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHDiv","instHSMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","Ad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e.spectral_ginibre_resolvent_spectrum_support","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.toSMul","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.ring","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFullComplexResolvent","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreSymmetricL2","HDiv.hDiv","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.right","IsScalarTower.to_smulCommClass'","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instIsScalarTower","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Lp.instNormedSpace._proof_1","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instDivInvMonoid","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Icc","Set.instLE","Set.instSingletonSet","Set.instUnion","SetLike.instMembership","Singleton.singleton","SubNegMonoid.toAddMonoid","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.isScalarTower'","Submodule.isTopologicalAddGroup","Submodule.module","Submodule.module'","Submodule.module._proof_1","Submodule.normedSpace","Submodule.seminormedAddCommGroup","Submodule.setLike","Submodule.zero","Subtype","Subtype.pseudoMetricSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Union.union","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instDistribOfSemiring","instHDiv","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopologicalSpaceSubtype","instUniformSpaceSubtype","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass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ocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalCommSemiring","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalRingHomClass.toMulHomClass","NonUnitalSemiring.toSemigroupWithZero","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","Not","OfNat.ofNat","One.toOfNat1","RCLike.toDenselyNormedField","RCLike.toNormedAlgebra","Real","Real.instDivInvMonoid","Real.instField","Real.instMonoid","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.normedField","Real.sqrt","Real.sqrt_one","Ring.toAddGroupWithOne","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toNonUnitalRingHomClass","RingHomCompTriple.comp_apply","RingHomInvPair.instStarRingEnd","RingHomInvPair.triples\u2082","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SeminormedCommRing.toSeminormedRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","True","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GaussianDbarParseval.0.GinibrePoincare.mixedMomentFormula_of_pos","_private.GinibrePoincare.Analysis.GaussianDbarParseval.0.GinibrePoincare.sqrt_mul_integral_coordinate_mul_normalizedEval._simp_1_1","congr","congrArg","congrFun'","div_one","eq_self","funext","id","instDecidableAnd","instDecidableEqNat","instDistribOfSemiring","instHDiv","instHMul","instHPow","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat","ite","ite_congr","map_mul","mul_assoc","of_eq_true","pow_one","starRingEnd"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreEntropy","name":"GinibrePoincare.squareEntropy","type_dependencies":["MeasurableSpace","MeasureTheory.Measure","Real"],"value_dependencies":["HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.log","Real.normedAddCommGroup","instHMul","instHPow","instHSub","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntropy","name":"GinibrePoincare.squareEntropy.eq_1","type_dependencies":["Eq","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.log","Real.normedAddCommGroup","instHMul","instHPow","instHSub","instOfNatNat"],"value_dependencies":["Eq.refl","GinibrePoincare.squareEntropy","MeasurableSpace","MeasureTheory.Measure","Real"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SquareEntropyLinearization","name":"GinibrePoincare.squareEntropy_affine_bound_variance","type_dependencies":["DivInvMonoid.toDiv","GinibrePoincare.squareEntropy","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Measurable","MeasurableSpace","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","One.toOfNat1","RCLike.toInnerProductSpaceReal","Real","Real.instAdd","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.lattice","Real.measurableSpace","Real.normedAddCommGroup","Zero.toOfNat0","abs","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Bool","Bool.false","Bool.true","BorelSpace.opensMeasurable","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toCommSemiring","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Ring","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.log","Real.log_one","Real.log_pow","Real.measurableSpace","Real.metricSpace","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","Set.univ","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","T5Space.toT1Space","T6Space.toT5Space","TopologicalSpace","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_nonneg","abs_of_nonneg","addRightReflectLE_of_addLeftReflectLE","add_zero","congr","congrArg","congrFun'","congr_arg","congr_arg\u2082","contravariant_lt_of_covariant_le","deriv","div_one","eq_of_heq","eq_self","funext","hasDerivAt_id","heq_of_eq","id","inferInstance","instAddNat","instDecidableEqNat","instDecidableNot","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instIsCancelMulZero","instIsRightCancelAddOfAddRightReflectLE","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNeZeroNatHAdd_1","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSecondCountableTopologyReal","instSubNat","instT6SpaceOfMetrizableSpace","le_of_not_gt","mul_nonneg_of_nonpos_of_nonpos","mul_one","neg_eq_zero","nhds","not_false_eq_true","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","one_ne_zero._simp_1","one_pow","rfl","sq_abs","sq_nonneg","sub_eq_zero_of_eq","sub_left_inj._simp_1","sub_self","zero_add","zero_pow"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialSobolevClosure","name":"GinibrePoincare.squareEntropy_congr_ae","type_dependencies":["Eq","Filter.EventuallyEq","GinibrePoincare.squareEntropy","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Real"],"value_dependencies":["Eq","Eq.mpr","Eq.refl","Filter.Eventually.mono","Filter.EventuallyEq","GinibrePoincare.squareEntropy_eq_of_moments","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.integral_congr_ae","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.log","Real.normedAddCommGroup","congrArg","id","instHMul","instHPow","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntropy","name":"GinibrePoincare.squareEntropy_eq_of_moments","type_dependencies":["Eq","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.log","Real.normedAddCommGroup","instHMul","instHPow","instOfNatNat"],"value_dependencies":["Eq","Eq.trans","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.integral","Monoid.toNPow","NPow.toPow","Nat","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instSub","Real.log","Real.normedAddCommGroup","True","congr","congrArg","congrFun'","eq_self","instHMul","instHPow","instHSub","instOfNatNat","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.EntropyL2Closure","name":"GinibrePoincare.squareEntropy_le_of_L2_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","ENNReal","ENNReal.instAddCommMonoidWithOne","Filter.Tendsto","Filter.atTop","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","LE.le","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","Me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ologicalSpace","instHMul","instHPow","instOfNatNat","nhds"],"value_dependencies":["AEMeasurable.comp_aemeasurable","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And.intro","BorelSpace.opensMeasurable","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toPartialOrder","Continuous.comp_aestronglyMeasurable","Continuous.continuousAt","Continuous.measurable","ContinuousAt.tendsto","ContinuousENorm.toENorm","Countable.LindelofSpace","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.continuous_ofReal","ENNReal.instCompleteLinearOrder","ENNReal.instLE","ENNReal.instOrderBot","ENNReal.instOrderTop","ENNReal.instOrderTopology","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instTopologicalSpace","ENNReal.measurableSpace","ENNReal.measurable_ofReal","ENNReal.ofReal","ENNReal.ofReal_le_ofReal","ENNReal.ofReal_le_ofReal_iff","ENNReal.ofReal_lt_top","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Filter.Eventually","Filter.Eventually.of_forall","Filter.Tendsto","Filter.Tendsto.add","Filter.Tendsto.comp","Filter.Tendsto.liminf_eq","Filter.atTop","Filter.atTop_neBot","Filter.isBounded_ge_of_bot","Filter.isCobounded_ge_of_top","Filter.liminf","Filter.liminf_le_liminf","Filter.map","Filter.mp_mem","Filter.univ_mem'","Function.comp","GinibrePoincare.continuous_shiftedSquareLog","GinibrePoincare.shiftedSquareLog","GinibrePoincare.shiftedSquareLog_nonneg","GinibrePoincare.squareEntropy","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mp","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","IsTopologicalRing.toIsSemitopologicalRing","LE.le","LE.le.trans_lt","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Measurable.aemeasurable","Measurable.comp_aemeasurable","MeasurableSpace","MeasureTheory.AEStronglyMeasurable","MeasureTheory.AEStronglyMeasurable.aemeasurable","MeasureTheory.HasFiniteIntegral","MeasureTheory.Integrable","MeasureTheory.Integrable._auto_1","MeasureTheory.Integrable.fun_add","MeasureTheory.Integrable.sub","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.map","MeasureTheory.Measure.real","MeasureTheory.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ClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Pullback","name":"GinibrePoincare.stationaryEndpointL2Operator._proof_8","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.stationaryEndpointL2Pullback._proof_2","GinibrePoincare.stationaryEndpointL2Pullback._proof_3","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","ContinuousLinearMap.addCommGroup._proof_7","ENNReal","ENNReal.instAddCommMonoidWithOne","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Pullback","name":"GinibrePoincare.stationaryEndpointL2Operator._proof_9","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CompleteSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.stationaryEndpointL2Pullback._proof_2","GinibrePoincare.stationaryEndpointL2Pullback._proof_3","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","MeasurableSpace","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Measure","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instCompleteSpace","Real.normedAddCommGroup","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Sampling","name":"GinibrePoincare.stationaryEndpointL2Operator.congr_simp","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.ndrec","GinibrePoincare.stationaryEndpointL2Operator","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.ins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riviallyNormedField","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","EquivLike.toFunLike","Field.toCommRing","Field.toSemifield","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.comp","Filter.atTop","GinibrePoincare.stationaryEndpointL2Operator._proof_1","GinibrePoincare.stationaryEndpointL2Operator._proof_2","GinibrePoincare.stationaryEndpointL2Pullback","GinibrePoincare.stationaryEndpointL2Pullback._proof_2","GinibrePoincare.stationaryEndpointL2Pullback._proof_3","GinibrePoincare.stationaryEndpointL2Pullback_tendsto","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","LinearIsometry","LinearIsometry.instFunLike","LinearIsometry.toContinuousLinearMap","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearMap","LinearMap.instFunLike","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.IsFiniteMeasure","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.WeaklyRegular","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instPreorder","NegZeroClass.toZero","NormalSpace","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.instAddCommMonoid","Real.instCompleteSpace","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","SMulZeroClass.toSMul","SecondCountableTopology","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TopologicalSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","nhds","smulCommClass_self","starRingEnd"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Pullback","name":"GinibrePoincare.stationaryEndpointL2Pullback","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","ENNReal","ENNReal.instAddCommMonoidWithOne","LinearIsometry","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddHom.mk","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddZeroClass","AddZeroClass.toAddZero","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","GinibrePoincare.stationaryEndpointL2Pullback._proof_1","GinibrePoincare.stationaryEndpointL2Pullback._proof_2","GinibrePoincare.stationaryEndpointL2Pullback._proof_3","GinibrePoincare.stationaryEndpointL2Pullback._proof_4","GinibrePoincare.stationaryEndpointL2Pullback._proof_5","GinibrePoincare.stationaryEndpointL2Pullback._proof_6","GinibrePoincare.stationaryEndpointL2Pullback._proof_7","LinearIsometry.mk","LinearMap.mk","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","Membership.mem","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreStochasticTransitionL2Pullback","name":"GinibrePoincare.stationaryEndpointL2Pullback._proof_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","HSMul.hSMul","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHSMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddSubmonoidClass.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Function.comp","Function.hasSMul","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAs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ZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","deriv","differentiable_id","eq_of_heq","funext","hasDerivAt_id","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsTopologicalRingReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instOrderTopologyReal","instPolynormableSpace","instSMulOfMul","instSubNat","le_of_not_gt","monotoneOn_univ","mul_one","rfl"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticProjectionTensorization","name":"GinibrePoincare.successiveOrthogonalProjections","type_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","CompleteSpace","ContinuousLinearMap","InnerProductSpace","InnerProductSpace.toNormedSpace","List","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.id","DenselyNormedField.toNormedField","Field.toSemifield","GinibrePoincare.successiveOrthogonalProjections._proof_1","InnerProductSpace","InnerProductSpace.toNormedSpace","List","List.foldr","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProjectionTensorization","name":"GinibrePoincare.successiveOrthogonalProjections._proof_1","type_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"],"value_dependencies":["CommSemiring.toSemiring","DenselyNormedField.toNormedField","Field.toSemifield","NormedField.toField","RCLike.toDenselyNormedField","Real","Real.instRCLike","Real.semiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProjectionTensorization","name":"GinibrePoincare.successiveOrthogonalProjections.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","CompleteSpace","ContinuousLinearMap","Eq","GinibrePoincare.successiveOrthogonalProjections","InnerProductSpace","InnerProductSpace.toNormedSpace","List","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","CompleteSpace","ContinuousLinearMap","Eq","Eq.rec","Eq.refl","GinibrePoincare.successiveOrthogonalProjections","InnerProductSpace","InnerProductSpace.toNormedSpace","List","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProjectionTensorization","name":"GinibrePoincare.successiveOrthogonalProjections.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.id","DenselyNormedField.toNormedField","Eq","Field.toSemifield","GinibrePoincare.successiveOrthogonalProjections","GinibrePoincare.successiveOrthogonalProjections._proof_1","InnerProductSpace","InnerProductSpace.toNormedSpace","List","List.foldr","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Real","Real.instRCLike","R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omialEigenfunctionSpan","name":"GinibrePoincare.sumRadiusEvaluation._proof_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Eq","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.R_poly","GinibrePoincare.S_observable","HAdd.hAdd","Matrix.vecCons","Matrix.vecEmpty","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","OfNat.ofNat","Pi.addCommMonoid","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHAdd","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.nonAssocSemiring","AddMonoidHomClass.toAddHomClass","AddMonoidWithOne.toAddMonoid","AddSemigroup.toAdd","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Eq","Eq.trans","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.R_poly","GinibrePoincare.S_observable","HAdd.hAdd","Matrix.vecCons","Matrix.vecEmpty","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Pi.addCommMonoid","RingHom","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toAddMonoidHomClass","Semiring.toNonAssocSemiring","True","congrArg","congrFun'","eq_self","funext","instHAdd","instOfNatNat","map_add","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctionSpan","name":"GinibrePoincare.sumRadiusEvaluation._proof_2","type_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidAlgebra.nonAssocSemiring","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instSemiring","Complex.instStarRing","Complex.ofReal","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.R_poly","GinibrePoincare.S_observable","HSMul.hSMul","Matrix.vecCons","Matrix.vecEmpty","Module.toDistribMulAction","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","instHSMul","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidAlgebra.nonAssocSemiring","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instMul","Complex.instSemiring","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.trans","Fin","Finsupp","Finsupp.instAddZeroClass","GinibrePoincare.Configuration","GinibrePoincare.R_poly","GinibrePoincare.S_observable","HMul.hMul","HSMul.hSMul","Matrix.vecCons","Matrix.vecEmpty","Module.toDistribMulAction","MulZeroClass.toZero","MvPolynomial","MvPolynomial.eval","MvPolynomial.smul_eval","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.succ","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","True","congrArg","congrFun'","eq_self","funext","instDistribOfSemiring","instHMul","instHSMul","instOfNatNat","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctionSpan","name":"GinibrePoincare.sumRadiusEvaluation.eq_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddHom.mk","AddMonoid.toAddZeroClass","AddMonoidAlgebra.instAddCommMonoid","AddMonoidAlgebra.instModule","AddMonoidAlgebra.nonAssocSemiring","CommSemiring.toSemiring","Complex","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instSemiring","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Eq","Fin","Fins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.instAddCommMonoid","Complex.instZero","Eq","Fin","Finset","Finset.instSetLike","Finset.sum","Finsupp","Finsupp.instAddCommMonoid","Finsupp.support","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.activeHolomorphicDegrees","GinibrePoincare.coefficientsAtHolomorphicDegree","Membership.mem","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","OfNat.ofNat","Pi.instZero","Prod.snd","SetLike.instMembership","Zero.toOfNat0"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Complex","Complex.instAddCommMonoid","Complex.instDecidableEq","Complex.instSemiring","Complex.instZero","DFunLike.coe","Decidable.not_not._simp_1","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists","Exists.intro","False","False.elim","Fin","Fin.fintype","Finset","Finset.decidableMem","Finset.image","Finset.instSetLike","Finset.mem_image","Finset.sum","Finset.sum_eq_single","Finset.sum_eq_zero","Finsupp","Finsupp.ext","Finsupp.filter","Finsupp.filter_apply_neg","Finsupp.filter_apply_pos","Finsupp.instAddCommMonoid","Finsupp.instFunLike","Finsupp.lapply","Finsupp.mem_support_iff._simp_1","Finsupp.module","Finsupp.support","Fintype.decidablePiFintype","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.activeHolomorphicDegrees","GinibrePoincare.coefficientsAtHolomorphicDegree","GinibrePoincare.totalHolomorphicDegree","Iff.mpr","LinearMap","LinearMap.instFunLike","LinearMap.semilinearMapClass","Membership.mem","Module.toDistribMulAction","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Ne","Ne.symm","Not","OfNat.ofNat","Pi.instZero","Prod.fst","Prod.snd","RingHom","RingHom.id","RingHom.instFunLike","SemilinearMapClass.distribMulActionSemiHomClass","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","True","Zero.toOfNat0","and_false","and_self","congr","congrArg","congrFun'","dite","eq_false","eq_self","id","instDecidableAnd","instDecidableEqNat","instDecidableEqProd","ite","ite_eq_left","ite_eq_right","map_sum","not_false_eq_true","of_eq_true","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.sum_core_flux_divergence_eq_density_mul_pregenerator","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","Fin.fintype","Finset.sum","Finset.univ","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.ginibreLebesgueDensityReal","GinibrePoincare.ginibrePregenerator","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","HAdd.hAdd","HMul.hMul","InnerProductSpace.toNormedSpace","LT.lt","Nat","Nat.cast","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHAdd","instHMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","And","And.left","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Compl.compl","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENat","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","FloorRing.toFloorSemiring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"Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Real.sqrt","Real.sqrt_nonneg","Real.sqrt_pos_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toMonoidWithZero","Zero.toOfNat0","id","inferInstance","instHDiv","instHMul","instHPow","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","mul_nonneg","pow_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.L2RepresentativeBridges","name":"GinibrePoincare.summable_transformedCentered_positiveModeMass","type_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.positiveHermiteModeMass","GinibrePoincare.transformedCenteredObservableL2","LT.lt","Nat","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.pseudoMetricSpace","Summable","SummationFilter.unconditional","UniformSpace.toTopologicalSpace","instLTNat","instOfNatNat"],"value_dependencies":["GinibrePoincare.Configuration","GinibrePoincare.IsTheoremOneNineCore","GinibrePoincare.summable_positiveHermiteModeMass","GinibrePoincare.transformedCenteredObservableL2","LT.lt","Nat","OfNat.ofNat","Real","instLTNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreMassPositivity","name":"GinibrePoincare.support_vandermondeDensity_isOpen_nonempty","type_dependencies":["And","Complex","Complex.instNormedField","ENNReal","ENNReal.instZero","Fin","Function.support","GinibrePoincare.Configuration","GinibrePoincare.vandermondeDensity","IsOpen","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set.Nonempty","UniformSpace.toTopologicalSpace"],"value_dependencies":["And.intro","Compl.compl","Complex","Complex.continuous_normSq","Complex.instField","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.normSq","Complex.normSq_pos","Complex.normSq_pos._simp_1","Continuous","Continuous.comp","DFunLike.coe","DivisionSemiring.toGroupWithZero","EMetricSpace.metrizableSpace","ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_eq_zero._simp_1","ENNReal.ofReal_pos","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists.intro","Field.toSemifield","Fin","Function.support","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.continuous_vandermonde","GinibrePoincare.integerConfiguration","GinibrePoincare.integerConfiguration_collisionFree","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermonde_ne_zero_iff","GroupWithZero.toMonoidWithZero","Iff.mpr","IsClosed.isOpen_compl","IsOpen","IsOpen.preimage","LE.le","LT.lt","LT.lt.ne'","LinearOrder.toPartialOrder","Membership.mem","MetricSpace.toEMetricSpace","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Ne","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instNontrivial","Real.instZero","Real.linearOrder","Real.metricSpace","Real.pseudoMetricSpace","Real.semiring","Semifield.toDivisionSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.Nonempty","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.ofPred","Singleton.singleton","T5Space.toT1Space","T6Space.toT5Space","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.GinibreMassPositivity.0.GinibrePoincare.support_vandermondeDensity_isOpen_nonempty._simp_1_4","congrArg","funext","id","instMulZeroOneClassOfSemiring","instT6SpaceOfMetrizableSpace","isClosed_singleton","map_eq_zero._simp_1","not_le._simp_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.RadialConvolutionInvariance","name":"GinibrePoincare.symmetric_convolution","type_dependencies":["Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instSub","Complex.measurableSpace","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Pi.instSub","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.measurableSpace","ContinuousLinearMap.lsmul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Equiv.symm","EquivLike.toFunLike","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.IsSymmetric","GinibrePoincare.ParticlePermutation","GinibrePoincare.permutationMeasurableEquiv","GinibrePoincare.permutationMeasurableEquiv_apply","GinibrePoincare.permute","HMul.hMul","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableEquiv.piCongrLeft","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving","MeasureTheory.MeasurePreserving.integral_comp'","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.convolution_lsmul","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MeasureTheory.volume_measurePreserving_piCongrLeft","Module.toDistribMulAction","Nat","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instMul","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SubNegMonoid.toAddMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","Trans.trans","UniformSpace.toTopologicalSpace","congr","congrArg","funext","id","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instTransEq","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.TaylorDifferenceQuotient","name":"GinibrePoincare.taylor_first_order_bound","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Field.toSemifield","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instSub","Real.lattice","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","abs","deriv","instHAdd","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat","iteratedDeriv"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stOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.FiniteEntropyTensorization","name":"GinibrePoincare.uniformFiniteLSI_tensorization","type_dependencies":["DivInvMonoid.toDiv","Finset.sum","Finset.univ","Fintype","Fintype.card","GinibrePoincare.uniformFiniteEntropy","HAdd.hAdd","HDiv.hDiv","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nonempty","OfNat.ofNat","Prod","Prod.mk","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instNatCast","instFintypeProd","instHAdd","instHDiv","instHPow","instOfNatNat"],"value_dependencies":["AddGroup.existsAddOfLE","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Field.toSemifield","Finset","Finset.instSetLike","Finset.sum","Finset.sum_le_sum","Finset.univ","Fintype","Fintype.card","GinibrePoincare.uniformFiniteEntropy","GinibrePoincare.uniformFiniteEntropy_tensorization","HAdd.hAdd","HDiv.hDiv","HPow.hPow","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LE.le.trans","Lattice.toSemilatticeInf","Membership.mem","Monoid.toNPow","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instNatCast","Real.instPreorder","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","SetLike.instMembership","add_le_add","div_le_div_of_nonneg_right","instDistribLatticeOfLinearOrder","instFintypeProd","instHAdd","instHDiv","instHPow","instMulZeroClassOfSemiring","instOfNatNat","sq_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.BrownianIntegralContinuousModificationSubsequence","name":"GinibrePoincare.uniformProbabilityCauchy_exists_subsequence","type_dependencies":["And","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoid","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instTopologicalSpace","ENNReal.instZero","Exists","Filter.Tendsto","Filter.atTop","GT.gt","HAdd.hAdd","HSub.hSub","LT.lt","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Nat","Nat.instPreorder","Ne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.instPreorder","Prod.snd","Real","Real.instAddGroup","Real.instLT","Real.instSub","Real.instZero","Real.lattice","Set","Set.ofPred","StrictMono","SummationFilter.unconditional","Top.top","Zero.toOfNat0","abs","instAddNat","instHAdd","instHSub","instOfNatNat","nhds","tsum"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","And","And.intro","Classical.choose","Classical.choose_spec","DFunLike.coe","Decidable.byContradiction","DistribLattice.toLattice","ENNReal","ENNReal.instAddCommMonoid","ENNReal.instLinearOrder","ENNReal.instOrderTop","ENNReal.instOrderTopology","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instTopologicalSpace","ENNReal.instZero","ENNReal.tsum_le_tsum","Eq","Eq.mpr","Exists","Exists.intro","Filter.Eventually","Filter.Tendsto","Filter.Tendsto.eventually","Filter.atTop","Filter.eventually_atTop_prod_self","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.single_le_sum","Finset.sum","Finset.sum_range_succ","GT.gt","HAdd.hAdd","HSub.hSub","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans","LT.lt","LT.lt.le","Lattice.toSemilatticeSup","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Membership.mem","Nat","Nat.decLe","Nat.decLt","Nat.instAddCommMonoid","Nat.instCommSemiring","Nat.instIsOrderedAddMonoid","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.le_succ","Nat.lt_succ_self","Nat.zero_le","Ne","Not","OfNat.ofNat","OrderTopology.to_orderClosedTopology","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.instPreorder","Prod.mk","Prod.snd","Real","Real.instAddGroup","Real.instLT","Real.instSub","Real.instZero","Real.lattice","SemilatticeSup.toPartialOrder","Set","Set.ofPred","SetLike.instMembership","StarOrderedRing.toIsOrderedRing","StrictMono","StrictMono.monotone","SummationFilter.unconditional","Top.top","Zero.toOfNat0","_private.GinibrePoincare.Analysis.BrownianIntegralContinuousModificationSubsequence.0.GinibrePoincare.uniformProbabilityCauchy_exists_subsequence._proof_1_1","_private.GinibrePoincare.Analysis.BrownianIntegralContinuousModificationSubsequence.0.GinibrePoincare.uniformProbabili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ermonde_permute","Group.toDivInvMonoid","HAdd.hAdd","HMul.hMul","HasDistribNeg.toInvolutiveNeg","Int","Int.cast","Int.cast_neg","Int.cast_one","Int.instCommRing","Int.instMonoid","Int.units_eq_one_or","InvolutiveNeg.toNeg","Monoid.toMulOneClass","MonoidHom","MonoidHom.instFunLike","MonoidHomClass.toMulHomClass","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddMonoid","Real.instMul","Real.instNeg","Real.instOne","Real.instZero","Real.semiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Units","Units.instMulOneClass","Units.instNeg","Units.instOne","Units.val","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","eq_self","id","instDecidableEqFin","instHAdd","instHMul","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","map_mul","mul_neg","mul_one","neg_neg","neg_zero","of_eq_true","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreRadialGamma","name":"GinibrePoincare.vandermondeDensity_real_smul","type_dependencies":["Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","Eq","Field.toSemifield","Fin","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.vandermondeDegree","GinibrePoincare.vandermondeDensity","HMul.hMul","HPow.hPow","HSMul.hSMul","LE.le","Monoid.toNPow","NPow.toPow","Nat","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","RCLike.toNormedAlgebra","Real","Real.instLE","Real.instMonoid","Real.instZero","Real.normedField","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Zero.toOfNat0","instDistribOfSemiring","instHMul","instHPow","instHSMul","instMulNat","instOfNatNat"],"value_dependencies":["Algebra.toSMul","CommSemiring.toSemiring","Complex","Complex.instMul","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.normSq","Complex.normSq_ofReal","Complex.ofReal","DFunLike.coe","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_mul","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset.Ioi","Finset.card","Finset.sum","Finset.univ","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.globalPhase","GinibrePoincare.vandermonde","GinibrePoincare.vandermondeDegree","GinibrePoincare.vandermondeDegree_eq_sum_Ioi_card","GinibrePoincare.vandermondeDensity","GinibrePoincare.vandermondeWeight","GinibrePoincare.vandermonde_globalPhase","HMul.hMul","HPow.hPow","HSMul.hSMul","IsOrderedRing.toPosMulMono","LE.le","Monoid.toMulOneClass","Monoid.toNPow","MonoidHomClass.toMulHomClass","MonoidWithZero.toMonoid","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MonoidWithZeroHom.monoidWithZeroHomClass","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instAddCommMonoid","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","RCLike.toNormedAlgebra","Real","Real.instIsOrderedRing","Real.instLE","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instPreorder","Real.instZero","Real.instZeroLEOneClass","Real.normedField","Real.partialOrder","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toMonoid","Zero.toOfNat0","congrArg","eq_self","funext","id","instDistribOfSemiring","instHMul","instHPow","instHSMul","instMulNat","instMulZeroOneClassOfSemiring","instOfNatNat","map_mul","map_pow","of_eq_true","pow_mul","pow_nonneg","pow_two"]},{"kind":"definition","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.vandermondeFactor","type_dependencies":["Complex","Fin","GinibrePoincare.Configuration","Nat"],"value_dependencies":["Complex","Complex.instSub","Fin","GinibrePoincare.Configuration","HSub.hSub","Nat","instHSub"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"GinibrePoincare.vandermondeFactor.eq_1","type_dependencies":["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omplex.instAdd","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","HAdd.hAdd","Nat","instHAdd"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","CommRing.toCommMonoid","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.commRing","Complex.instAdd","Complex.instCommSemiring","Complex.instSub","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Fin","Fin.fintype","Fin.instLocallyFiniteOrderTop","Fin.instPartialOrder","Finset","Finset.Ioi","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","GinibrePoincare.vandermonde_eq_product","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder.toPreorder","Ring","Ring.toAddCommGroup","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreCenterProjectionEquality","name":"GinibrePoincare.vandermonde_centerOfMassReal_decomposition","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.instAdd","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instOne","Complex.instStarRing","Complex.ofReal","DFunLike.coe","DivInvMonoid.toDiv","Eq","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.coordinateSum","GinibrePoincare.vandermonde","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","instHAdd","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instOne","Complex.instStarRing","Complex.ofReal","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","GinibrePoincare.Configuration","GinibrePoincare.centerOfMassReal","GinibrePoincare.centerOfMassReal_complex_decomposition","GinibrePoincare.coordinateSum","GinibrePoincare.vandermonde","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.C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tMembership","Subtype","Subtype.instMeasurableSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instTopologicalSpaceSubtype","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.ring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Field.toSemifield","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.borelSpace","Real.instCommSemiring","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.borelSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","spectrum"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralMeasure._proof_3","type_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.ring","Field.toSemifield","GinibrePoincare.vectorSpectralPositiveFunctional._proof_3","GinibrePoincare.vectorSpectralPositiveFunctional._proof_5","GinibrePoincare.vectorSpectralPositiveFunctional._proof_6","GinibrePoincare.vectorSpectralPositiveFunctional._proof_7","InnerProductSpace","InnerProductSpace.toNormedSpace","LocallyCompactSpace","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","Subtype.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarAlgebra.toNormedAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instDenselyNormedField","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instCompleteSpace","ContinuousLinearMap.ring","ContinuousLinearMap.toNormedRing","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Field.toSemifield","FirstCountableTopology.frechetUrysohnSpace","FrechetUrysohnSpace.to_sequentialSpace","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toMetricSpace","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.complexToReal","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.to_isUniformAddGroup","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.pseudoMetricSpace","TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instPolynormableSpace","instProperSpaceReal","locallyCompact_of_proper","proper_of_compact","spectrum","spectrum.instCompactSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralMeasure.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Field.toSemifield","GinibrePoincare.vectorSpectralMeasure","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","MeasureTheory.Measure","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.instZero","Real.measurableSpace","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.Elem","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.instMeasurableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","spectrum"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.algebra","ContinuousLinearMap.instStarId","ContinuousLinearMap.ring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","Eq","Eq.rec","Eq.refl","Field.toSemifield","GinibrePoincare.vectorSpectralMeasure","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","IsSelfAdjoint","MeasureTheory.Measure","Membership.mem","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toMod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NonAssocCommRing.toNonUnitalNonAssocRing","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.metricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_11","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","Monoid.toSemigroup","MulAction.toSemigroupAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulCommClass","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","CommRing.toCommMonoid","Complex","Complex.commRing","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_12","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toSemigroup","MulAction.toSemigroupAction","MulOne.toMul","MulOneClass.toMulOne","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SemigroupAction.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toMulAction","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_13","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Complex.instNormedField","Complex.instRCLike","Complex.instZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.A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ralMeasure.0.GinibrePoincare.vectorSpectralPositiveFunctional._simp_3","cfcHom","cfcHom_mono","congrArg","id","inner_sub_right","instCStarAlgebraContinuousLinearMapComplexIdOfCompleteSpace","instCommCStarAlgebraComplex","instContinuousSqrtReal","instContinuousStarReal","instDistribOfSemiring","instHSub","instIsTopologicalRingReal","instSMulOfMul","instStarRingReal","instTopologicalSpaceSubtype","smulCommClass_self","spectrum","sub_nonneg"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_5","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","Real","Real.instCommSemiring","Real.normedField","SMulCommClass","SMulZeroClass.toSMul","Semiring.toMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","IsScalarTower.to_smulCommClass'","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedSpace.complexToReal","NormedSpace.toModule","RCLike.toNormedAlgebra","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","instCommCStarAlgebraComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_6","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower","Module.complexToReal","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsScalarTower.complexToReal","IsScalarTower.left","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","SMulZeroClass.toSMul","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_7","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","ContinuousConstSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","Module.toDistribMulAction","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.normedField","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","Complex","Complex.instRCLike","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","InnerProductSpace","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","Module.toDistribMulAction","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.complexToReal","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instCommSemiring","Real.instZero","Real.normedField","Real.pseudoMetricSpace","SMulZeroClass.toSMul","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformContinuousConstSMul.instContinuousConstSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_8","type_dependencies":["CommRing.toNonUnitalCommRing","ContinuousAdd","Distrib.toAdd","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","name":"GinibrePoincare.vectorSpectralPositiveFunctional._proof_9","type_dependencies":["ContinuousConstSMul","PseudoMetricSpace.toUniformSpace","Real","Real.instMul","Real.pseudoMetricSpace","UniformSpace.toTopologicalSpace","instSMulOfMul"],"value_dependencies":["CommRing.toNonUnitalCommRing","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instMul","Real.pseudoMetricSpace","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instIsTopologicalRingReal"]},{"kind":"definition","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingMonomialClosure","name":"GinibrePoincare.volumeAlternationOperator","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","Fin.fintype","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instInv","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.instSMul","DistribMulAction.toDistribSMul","ENNReal","ENNReal.instAddCommMonoidWithOne","Equiv.instFintype","Fin","Fin.fintype","Finset.sum","Finset.univ","Fintype.card","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.configurationVolume","GinibrePoincare.permutationSign","GinibrePoincare.volumeAlternationOperator._proof_1","GinibrePoincare.volumeAlternationOperator._proof_10","GinibrePoincare.volumeAlternationOperator._proof_2","GinibrePoincare.volumeAlternationOperator._proof_3","GinibrePoincare.volumeAlternationOperator._proof_4","GinibrePoincare.volumeAlternationOperator._proof_5","GinibrePoincare.volumeAlternationOperator._proof_8","GinibrePoincare.volumeAlternationOperator._proof_9","GinibrePoincare.volumePermutationL2","HSMul.hSMul","Inv.inv","LinearIsometry.toContinuousLinearMap","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.cast","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedField.toNormedCommRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instDecidableEqFin","instHSMul","instOfNatAtLeastTwo"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingMonomialClosure","name":"GinibrePoincare.volumeAlternationOperator._proof_1","type_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticAlternatingMonomialClosure","name":"GinibrePoincare.volumeAlternationOperator._proof_10","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ContinuousAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationVolume","GinibrePoincare.volumeAlternationOperator._proof_1","GinibrePoincare.volumeAlternationOperator._proof_2","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","SubNegMonoid.toAddMonoid","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instOfNatAtLeastTwo"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","Complex","Complex.instNormedAddCommGroup","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Fin","GinibrePoincare.Configuration","GinibrePoincare.configurationVolume","IsTopologicalAddGroup.toContinuousAdd","MeasurableSpace.pi","Me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instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","Exists","Field.toSemifield","Filter.EventuallyEq","Fin","Fin.fintype","Fintype","GinibrePoincare.Configuration","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_1","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_2","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_3","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.ae","Membership.mem","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set.ofPred","SetLike.instMembership","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","fderiv","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevWeightedCompact","name":"GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_1","type_dependencies":["AddCommGroup.toAddGroup","IsTopologicalAddGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevWeightedCompact","name":"GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_2","type_dependencies":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixSpectralSobolevWeightedCompact","name":"GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_3","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.OuterMeasureClass","Nat"],"value_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","MeasurableSpace.pi","MeasureTheory.Measure.instOuterMeasureClass","Nat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIScaling","name":"GinibrePoincare.weightedH1Completion_lsi_of_C2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","And","CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.compactC1SobolevPairs","GinibrePoincare.squareEntropy","HMul.hMul","HPow.hPow","HasCompactSupport","InnerProductSpace.toNormedSpace","LE.le","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Integrable","MeasureTheory.IsProbabilityMeasure","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.integral","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat"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rePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.piPlanarBump","GinibrePoincare.piPlanarBump._proof_1","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.planarComplexCompactTestSpace","GinibrePoincare.planarComplexTestTranslate","GinibrePoincare.planarPiNormalizedBumpTest","GinibrePoincare.planarPiNormalizedBumpTest._proof_1","GinibrePoincare.planarPiNormalizedBumpTest._proof_2","GinibrePoincare.planarPiPureDbarGraph","GinibrePoincare.planarPiTranslatedGraph_integral_value_ae","GinibrePoincare.weightedPiBumpAverage","GinibrePoincare.weightedPiBumpAverage._proof_1","GinibrePoincare.weightedPiBumpAverage._proof_3","GinibrePoincare.weightedPiBumpAverage._proof_4","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod.fst","Prod.instSMul","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Submodule","Submodule.setLike","Subtype","Subtype.mk","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","fact_one_le_two_ennreal","funext","id","instAddNat","instHAdd","instHMul","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticPiWeightedMollification","name":"GinibrePoincare.weightedPiBumpAverage_tendsto","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","ContDiffBump","ContDiffBump.rOut","Continuous","Continuous.mul","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Filter.Tendsto","Filter.atTop","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.piCompactFunctionL2","GinibrePoincare.piPotentialHalfWeight","GinibrePoincare.piPotentialHalfWeight_continuous","GinibrePoincare.weightedPiBumpAverage","HAdd.hAdd","HMul.hMul","HasCompactSupport","HasCompactSupport.mul_right","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instPreorder","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminorme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ZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","instMulZeroClassOfSemiring"],"value_dependencies":["Complex","Complex.instNormedField","Complex.instRCLike","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","RCLike.innerProductSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification","name":"GinibrePoincare.weightedProductBumpAverage._proof_8","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.measurableSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.SFinite","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification","name":"GinibrePoincare.weightedProductBumpAverage._proof_9","type_dependencies":["Complex","Complex.instNormedAddCommGroup","HasContDiffBump","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.instRCLike","instInnerProductSpaceRealComplex"],"value_dependencies":["Complex","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","InnerProductSpace.toNormedSpace","NormedAddCommGroup.toSeminormedAddCommGroup","Real","Real.instRCLike","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification","name":"GinibrePoincare.weightedProductBumpAverage.eq_1","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.normed","Continuous","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","GinibrePoincare.l2ProductVector","GinibrePoincare.planarWeightedTranslateL2","GinibrePoincare.weightedProductBumpAverage","GinibrePoincare.weightedProductBumpAverage._proof_1","GinibrePoincare.weightedProductBumpAverage._proof_2","GinibrePoincare.weightedProductBumpAverage._proof_3","GinibrePoincare.weightedProductBumpAverage._proof_4","GinibrePoincare.weightedProductBumpAverage._proof_5","GinibrePoincare.weightedProductBumpAverage._proof_6","GinibrePoincare.weightedProductBumpAverage._proof_7","GinibrePoincare.weightedProductBumpAverage._proof_8","GinibrePoincare.weightedProductBumpAverage._proof_9","HSMul.hSMul","InnerProductSpace.toNormedSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instNormedSpace","MeasureTheory.Measure.prod","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.to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nstHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instTopENat","instTopologicalSpaceProd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Algebra.id","And","And.casesOn","And.intro","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContDiff","Continuous","Continuous.comp","Continuous.prodMk","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.continuous","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCommSemiring","ENNReal.instTop","ENat","Eq","Eq.mp","Exists.casesOn","Exists.intro","Field.toSemifield","Filter.EventuallyEq","Filter.EventuallyEq.symm","Filter.EventuallyEq.trans","Fin","Fin.fintype","Fintype","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.configurationCompactDirectionalPairs","GinibrePoincare.configurationCompactDirectionalPairs._proof_1","GinibrePoincare.configurationCompactDirectionalPairs._proof_2","GinibrePoincare.configurationCompactDirectionalPairs._proof_3","GinibrePoincare.configuration_compact_weak_pair_mem_directional_closure","GinibrePoincare.weightedConfigurationCompactDirectionalPairs","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_1","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_2","GinibrePoincare.weightedConfigurationCompactDirectionalPairs._proof_3","HMul.hMul","HSMul.hSMul","HasCompactSupport","InnerProductSpace.toNormedSpace","IsClosed.preimage","IsScalarTower.right","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.LpToLpOfMeasureLeSMul","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_LpToLpOfMeasureLeSMul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.Measure.AbsolutelyContinuous","MeasureTheory.Measure.AbsolutelyContinuous.ae_eq","MeasureTheory.Measure.absolutelyContinuous_of_le_smul","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instPartialOrder","MeasureTheory.Measure.instSMul","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.of_measure_le_smul","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instMul","Real.instNeg","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.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dZero","Eq","Eq.rec","Eq.refl","Homeomorph","Homeomorph.addRight","SeparatelyContinuousAdd","SubNegMonoid.toAddMonoid","TopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientLocal","name":"Homeomorph.subLeft.congr_simp","type_dependencies":["AddGroup","Eq","Homeomorph","Homeomorph.subLeft","IsTopologicalAddGroup","TopologicalSpace"],"value_dependencies":["AddGroup","Eq","Eq.rec","Eq.refl","Homeomorph","Homeomorph.subLeft","IsTopologicalAddGroup","TopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialEigenfunctionBasis","name":"LinearEquiv.ofEq.eq_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddHom.mk","Eq","Equiv.invFun","Equiv.toFun","LinearEquiv","LinearEquiv.mk","LinearEquiv.ofEq","LinearEquiv.ofEq._proof_1","LinearEquiv.ofEq._proof_2","LinearEquiv.ofEq._proof_3","LinearEquiv.ofEq._proof_4","LinearEquiv.ofEq._proof_5","LinearMap.mk","Membership.mem","Module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring","Set.Elem","Set.equivOfEq","SetLike.coe","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype"],"value_dependencies":["AddCommMonoid","Eq","Eq.refl","LinearEquiv","LinearEquiv.ofEq","Membership.mem","Module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibrePermutationGradient","name":"LinearEquiv.piCongrLeft.eq_1","type_dependencies":["AddCommMonoid","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","LinearEquiv","LinearEquiv.piCongrLeft","LinearEquiv.piCongrLeft'","LinearEquiv.symm","Module","Pi.addCommMonoid","Pi.module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring"],"value_dependencies":["AddCommMonoid","DFunLike.coe","Eq.refl","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","LinearEquiv","LinearEquiv.piCongrLeft","Module","Pi.addCommMonoid","Pi.module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianBlockLSI","name":"LinearEquiv.piCurry.eq_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddHom.mk","Eq","Equiv.invFun","Equiv.piCurry","Equiv.toFun","LinearEquiv","LinearEquiv.mk","LinearEquiv.piCurry","LinearEquiv.piCurry._proof_1","LinearEquiv.piCurry._proof_2","LinearEquiv.piCurry._proof_3","LinearEquiv.piCurry._proof_4","LinearMap.mk","Module","Pi.addCommMonoid","Pi.module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring","Sigma","Sigma.fst","Sigma.snd"],"value_dependencies":["AddCommMonoid","Eq.refl","LinearEquiv","LinearEquiv.piCurry","Module","Pi.addCommMonoid","Pi.module","RingHom.id","RingHomInvPair.ids","Semiring","Semiring.toNonAssocSemiring","Sigma","Sigma.fst","Sigma.snd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"LinearEquiv.smulOfNeZero.eq_1","type_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","DivisionSemiring.toGroupWithZero","Eq","Field","Field.toSemifield","LinearEquiv","LinearEquiv.smulOfNeZero","LinearEquiv.smulOfUnit","Module","MulZeroClass.toZero","Ne","OfNat.ofNat","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","Units.mk0","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Eq.refl","Field","Field.toSemifield","LinearEquiv","LinearEquiv.smulOfNeZero","Module","MulZeroClass.toZero","Ne","OfNat.ofNat","RingHom.id","RingHomInvPair.ids","Semifield.toCommSemiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instMulZeroClassOfSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"LinearEquiv.smulOfUnit.eq_1","type_dependencies":["AddCommMonoid","AddCommMonoid.toAddMonoid","CommSemiring","CommSemiring.toSemiring","DistribMulAction.toLinearEquiv","Eq","LinearEquiv","LinearEquiv.smulOfUnit","LinearEquiv.smulOfUnit._proof_1","Module","Module.toDistribMulAction","RingHom.id","RingHomInvPair.ids","Semiring.toMonoid","Semiring.toNonAssocSemiring","Units","Units.instDistribMulAction","Units.instGroup"],"value_dependencies":["AddCommMonoid","CommSemiring","CommSemiring.toSemiring","Eq.refl","LinearEquiv","LinearEquiv.smulOfUnit","Module","RingHom.id","RingHomInvPair.ids","Semiring.toMonoid","Semiring.toNonAssocSemiring","Units"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianFourierCoordinates","name":"LinearEquiv.toContinuousLinearEquiv.congr_simp","type_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearEquiv","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Field.toDivisionRing","Field.toSemifield","FiniteDimensional","IsTopologicalAddGroup","LinearEquiv","LinearEquiv.toContinuousLinearEquiv","Module","Module.toDistribMulAction","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","T2Space","TopologicalSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","CompleteSpace","ContinuousLinearEquiv","ContinuousSMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Eq.rec","Eq.refl","Field.toDivisionRing","Field.toSemifield","FiniteDimensional","IsTopologicalAddGroup","LinearEquiv","LinearEquiv.toContinuousLinearEquiv","Module","Module.toDistribMulAction","NontriviallyNormedField","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","RingHom.id","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","T2Space","TopologicalSpace","UniformSpace.toTopologicalSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianGaussianCoordinateLaw","name":"MeasurableEquiv.curry.eq_1","type_dependencies":["Eq","Equiv.curry","MeasurableEquiv","MeasurableEquiv.curry","MeasurableEquiv.curry._proof_2","MeasurableEquiv.curry._proof_4","MeasurableEquiv.mk","MeasurableSpace","MeasurableSpace.pi","Prod"],"value_dependencies":["Eq.refl","MeasurableEquiv","MeasurableEquiv.curry","MeasurableSpace","MeasurableSpace.pi","Prod"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianPolynomialIntegrability","name":"MeasurableEquiv.finTwoArrow.eq_1","type_dependencies":["Eq","Fin","MeasurableEquiv","MeasurableEquiv.finTwoArrow","MeasurableEquiv.piFinTwo","MeasurableSpace","MeasurableSpace.pi","Nat","OfNat.ofNat","Prod","Prod.instMeasurableSpace","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","MeasurableEquiv","MeasurableEquiv.finTwoArrow","MeasurableSpace","MeasurableSpace.pi","Nat","OfNat.ofNat","Prod","Prod.instMeasurableSpace","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixPolynomialNull","name":"MeasurableEquiv.piFinSuccAbove.eq_1","type_dependencies":["Eq","Equiv.symm","Fin","Fin.insertNthEquiv","Fin.succAbove","HAdd.hAdd","MeasurableEquiv","MeasurableEquiv.mk","MeasurableEquiv.piFinSuccAbove","MeasurableEquiv.piFinSuccAbove._proof_1","MeasurableEquiv.piFinSuccAbove._proof_4","MeasurableSpace","MeasurableSpace.pi","Nat","OfNat.ofNat","Prod","Prod.instMeasurableSpace","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["Eq.refl","Fin","Fin.succAbove","HAdd.hAdd","MeasurableEquiv","MeasurableEquiv.piFinSuccAbove","MeasurableSpace","MeasurableSpace.pi","Nat","OfNat.ofNat","Prod","Prod.instMeasurableSpace","instAddNat","instHAdd","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GeneralRadialProjectionPhase","name":"MeasureTheory.Lp.compMeasurePreserving\u2097\u1d62.congr_simp","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddSubgroup","AddSubgroup.instSetLike","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instLE","ENNReal.instOne","Eq","Eq.ndrec","Fact","IsBoundedSMul","LE.le","LinearIsometry","MeasurableSpace","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.compMeasurePreserving\u2097\u1d62","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure","MeasureTheory.MeasurePreserving","Membership.mem","Module","Module.toDistribMulAction","MulZeroClass.toZero","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Seminor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v","instHMul","instHPow","instHSub","instIsCancelMulZero","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","mul_one","neg_mul","of_decide_eq_true","one_mul","one_ne_zero","rfl"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryCameronMartin","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryCameronMartin.0.GinibrePoincare.responseRegularized_pos","type_dependencies":["LE.le","LT.lt","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instZero","Zero.toOfNat0","_private.GinibrePoincare.Analysis.AlternativeBakryEmeryCameronMartin.0.GinibrePoincare.responseRegularized"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.addLeftReflectLE_of_addLeftMono","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.bakryEmeryResponseCovariance","GinibrePoincare.bakryEmeryResponseCovariance._proof_1","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.exp","Real.exp_le_one_iff","Real.exp_pos","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","addRightReflectLE_of_addLeftReflectLE","add_pos_of_nonneg_of_pos","congrArg","c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sureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Nat","Nat.cast_one","Nat.cast_zero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instDivisionRing","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","fderiv","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHAdd","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOneENat","instZeroENat","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsLSIContraction","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsLSIContraction.0.GinibrePoincare.bakryEmeryLangevinEndpoint_synchronous_norm._simp_1_1","type_dependencies":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dependencies":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalAction.0.GinibrePoincare.gibbsRelative_contDiff","type_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsRelativePotential","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","Pi.normedAddCommGroup","Pi.normedSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","WithTop","WithTop.natCast","instCommCStarAlgebraComplex","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["CommCStarAlgebra.toNormedCommRing","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.mul","ContDiff.of_le","ContDiff.sub","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Eq.trans","False","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","HMul.hMul","InnerProductSpace.toNormedSpace","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toSeminormedRing","Not","OfNat.ofNat","OrderTop.toTop","Pi.normedAddCommGroup","Pi.normedSpace","Preorder.toLE","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instMul","Real.instNatCast","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","SeminormedCommRing.toNonUnitalSeminormedCommRing","Top.top","True","WithTop","WithTop.instPreorder","WithTop.le_coe_top._simp_1","WithTop.natCast","WithTop.ofNat_ne_top._simp_1","WithTop.some","WithTop.top","congrArg","contDiff_const","instAddMonoidWithOneENat","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instOrderTopENat","instPreorderENat","instTopENat","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalCoupling","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalCoupling.0.GinibrePoincare.bakryEmeryGibbs_actual_stopped_coupling._abel_1_3","type_dependencies":["Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.ginibreBrownianFullContinuousNoise","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Pi.instAdd","Pi.instSub","Pi.instZero","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.instZero","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Distrib.toAdd","Eq","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.ginibreBrownianFullContinuousNoise","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Pi.addCommGroup","Pi.addZeroClass","Pi.instAdd","Pi.instNeg","Pi.instSub","Pi.instZero","Pi.negZeroClass","Pi.normedAddCommGroup","Pi.normedSpace","Pi.subtractionMonoid","Pi.topologicalSpace","Prod","PseudoMetricSpace.toUniformSpace","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.pseudoMetricSpace","Real.toNNReal","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalVolterra","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryGibbsReversalVolterra.0.GinibrePoincare.bakryEmeryGibbsOU_correctedBrownian_volterra._abel_1_1","type_dependencies":["Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Eq","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.ginibreConfigurationBrownianNoise","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Prod","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.toNNReal","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Zero.toOfNat0","instCommCStarAlgebraComplex","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Algebra.toSMul","CommCStarAlgebra.toNormedCommRing","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.instSub","Complex.instZero","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Function.hasSMul","GinibrePoincare.Configuration","GinibrePoincare.bakryEmeryGibbsConfigurationDrift","GinibrePoincare.ginibreConfigurationBrownianNoise","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedCommRing.toSeminormedCommRing","NormedField.toField","OfNat.ofNat","Pi.addCommGroup","Pi.addZeroClass","Pi.instAdd","Pi.instNeg","Pi.instSub","Pi.instZero","Pi.negZeroClass","Pi.normedAddCommGroup","Pi.normedSpace","Pi.subtractionMonoid","Prod","RCLike.toNormedAlgebra","Real","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Real.toNNReal","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instCommCStarAlgebraComplex","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instInnerProductSpaceRealComplex","instOfNat","instOfNatAtLeastTwo","instOfNatNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinConfiguration","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinConfiguration.0.GinibrePoincare.bakryEmery_configuration_volterra_identification._simp_1_1","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinConfiguration","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinConfiguration.0.GinibrePoincare.bakryEmery_configuration_volterra_prefix_identification._simp_1_1","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobal","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobal.0.GinibrePoincare.bakryEmeryLangevin_global_exists_on._simp_1_1","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobalContinuity","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobalContinuity.0.GinibrePoincare.bakryEmeryLangevinPath_lipschitzOn_bounded._abel_1_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","ContinuousMap","Eq","GinibrePoincare.bkWeightedExtension","HAdd.hAdd","HSub.hSub","LE.le","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toSub","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSub","instTopologicalSpaceSubtype"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","ContinuousMap","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.bkWeightedExtension","HAdd.hAdd","HSub.hSub","Int","Int.instNegInt","LE.le","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Membership.mem","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","Prod","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instPreorder","Real.instZero","Real.pseudoMetricSpace","SeminormedAddCommGroup.toPseudoMetricSpace","Set","Set.Elem","Set.Icc","Set.instMembership","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instHAdd","instHSub","instOfNat","instTopologicalSpaceSubtype","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobalContinuity","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryLangevinGlobalContinuity.0.GinibrePoincare.bakryEmeryLangevinStateOn_spec._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CompleteSpace","ContDiff","ContinuousMap","ConvexOn","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","FiniteDimensional","GinibrePoincare.bakryEmeryLangevinCorrectionOn","GinibrePoincare.bakryEmeryLangevinDrift","GinibrePoincare.bakryEmeryLangevinStateOn._proof_2","GinibrePoincare.bkWeightedExtension","GinibrePoincare.bkWeightedExtension_continuous","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace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oid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","EuclideanSpace","Function.hasSMul","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","Module.toDistribMulAction","Nat","Nat.cast","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.distribMulAction","PiLp.innerProductSpace._proof_1","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRing","Real.instSub","Real.semiring","Ring.toSemiring","SMulZeroClass.toSMul","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","WithLp.instAddCommGroup","WithLp.instDistribMulAction","WithLp.instModule","WithLp.instSMul","instAddNat","instHAdd","instHDiv","instHMul","instHSMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Eq.symm","Eq.trans","EuclideanSpace","Function.hasSMul","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSMul.hSMul","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","Module.toDistribMulAction","Nat","Nat.cast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.distribMulAction","PiLp.innerProductSpace._proof_1","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRing","Real.instSub","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","WithLp.instAddCommGroup","WithLp.instDistribMulAction","WithLp.instModule","WithLp.instSMul","Zero.toOfNat0","add_zero","instAddNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSMul","instHSub","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryPolygonalApproximation","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryPolygonalApproximation.0.GinibrePoincare.bakryEmeryPolygonalNoise_sampled_error._simp_1_1","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeBakryEmeryPolygonalApproximation","name":"_private.GinibrePoincare.Analysis.AlternativeBakryEmeryPolygonalApproximation.0.GinibrePoincare.bakryEmeryPolygonalNoise_sampled_grid._proof_1_10","type_dependencies":["And","False","Iff","LE.le","LT.lt","Nat","Not","instLENat","instLTNat"],"value_dependencies":["And","And.left","And.right","Bool","Bool.true","Classical.propDecidable","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Decidable.and_not_or_not_and_of_not_iff","Lean.Omega.Decidable.or_not_not_of_not_and","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omeg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sReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterExpansion","name":"_private.GinibrePoincare.Analysis.AlternativeSlaterExpansion.0.GinibrePoincare.slaterDegreeMass_eq_mode_norm._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterExpansion","name":"_private.GinibrePoincare.Analysis.AlternativeSlaterExpansion.0.GinibrePoincare.slaterDegreeMass_eq_mode_norm._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSlaterLowering","name":"_private.GinibrePoincare.Analysis.AlternativeSlaterLowering.0.GinibrePoincare.slater_dbar_const_mul","type_dependencies":["CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.dbarComponent","GinibrePoincare.dbarComponent._proof_1","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toInv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","M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"NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.isScalarTower","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","RingHomInvPair.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SemigroupAction.toSMul","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","eq_self","funext","id","instInnerProductSpaceRealComplex","map_zero","of_eq_true","starRingEnd","starRingEnd_self_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralDifferentialFactorization","name":"_private.GinibrePoincare.Analysis.AlternativeSpectralDifferentialFactorization.0.GinibrePoincare.spectral_complex_differential_factorization._simp_1_1","type_dependencies":["Distrib.toMul","Eq","Finset","Finset.sum","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"],"value_dependencies":["Distrib.toMul","Eq.symm","Finset","Finset.mul_sum","Finset.sum","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial","name":"_private.GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial.0.GinibrePoincare.spectralNumberCoefficients_eq_sum._simp_1_1","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.module","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.loweredCoefficients","GinibrePoincare.spectralLoweringCoefficients","LinearMap","LinearMap.instFunLike","Nat","RingHom.id","Semiring.toModule","Semiring.toNonAssocSemiring"],"value_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instSemiring","Complex.instZero","DFunLike.coe","Eq.symm","Fin","Finsupp","Finsupp.instAddCommMonoid","Finsupp.module","GinibrePoincare.ComplexHermite.HermiteMultiIndex","GinibrePoincare.ComplexHermite.loweredCoefficients","GinibrePoincare.spectralLoweringCoefficients","GinibrePoincare.spectralLoweringCoefficients_eq","LinearMap","LinearMap.instFunLike","Nat","RingHom.id","Semiring.toModule","Semiring.toNonAssocSemiring"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial","name":"_private.GinibrePoincare.Analysis.AlternativeSpectralNumberPolynomial.0.GinibrePoincare.spectralPartial_const_mul","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.bkPartial","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSub","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.i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ance","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instLTNat","instOfNatNat","instPerfectSpace","instT6SpaceOfMetrizableSpace","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CollisionNull","name":"_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.coordinate_diagonal_null","type_dependencies":["Complex","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instZero","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","LT.lt","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","Nat","Ne","OfNat.ofNat","Set","Set.ofPred","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["Complex","Complex.borelSpace","Complex.instCompleteSpace","Complex.instNormedField","Complex.instProperSpace","Complex.measurableSpace","DFunLike.coe","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","ENNReal","ENNReal.instZero","Eq","Eq.mpr","Eq.symm","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","LT.lt","Measurable","Measurable.prodMk","MeasurableEq.measurableSet_diagonal","MeasurableSet","MeasurableSpace.pi","MeasureTheory.IsFiniteMeasure.toIsLocallyFiniteMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.map","MeasureTheory.Measure.map_apply","MeasureTheory.Measure.prod","MeasureTheory.ProbabilityMeasure.instIsProbabilityMeasureToMeasure","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.sigmaFinite_of_locallyFinite","MetricSpace.toEMetricSpace","Nat","Ne","NormedCommRing.toSeminormedCommRing","NormedField.toMetricSpace","NormedField.toNormedCommRing","OfNat.ofNat","Prod","Prod.instMeasurableSpace","Prod.mk","PseudoMetricSpace.toUniformSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.diagonal","Set.ofPred","Set.preimage","StandardBorelSpace.instMeasurableEq","T6Space.toT0Space","TopologicalSpace.IsCompletelyMetrizableSpace.of_completeSpace_metrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.complexCoordinateGaussian_nullSingleton","_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.coordinate_pair_map","_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.measure_prod_diagonal_eq_zero","congrArg","id","instLTNat","instOfNatNat","instPolishSpaceOfSeparableSpaceOfIsCompletelyMetrizableSpace","instT6SpaceOfMetrizableSpace","measurable_pi_apply","secondCountable_of_proper","standardBorel_of_polish"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CollisionNull","name":"_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.coordinate_pair_map","type_dependencies":["Complex","Complex.measurableSpace","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","MeasurableSpace.pi","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.prod","MeasureTheory.ProbabilityMeasure.toMeasure","Nat","Ne","Prod","Prod.instMeasurableSpace","Prod.mk"],"value_dependencies":["Complex","Complex.measurableSpace","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Fin","Fin.fintype","Fintype","Function.eval","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianProbability","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.complexGaussianProbability","GinibrePoincare.instIsProbabilityMeasureComplexGaussianMeasure","Measurable.aemeasurable","MeasurableSpace","MeasurableSpace.pi","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.map","MeasureTheory.Measure.map_id","MeasureTheory.Measure.pi","MeasureTheory.Measure.prod","MeasureTheory.MeasurePreserving.map_eq","MeasureTheory.ProbabilityMeasure.instIsProbabilityMeasureToMeasure","MeasureTheory.ProbabilityMeasure.pi","MeasureTheory.ProbabilityMeasure.toMeasure","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.measurePreserving_eval","Nat","Ne","ProbabilityTheory.IndepFun.map_prod_eq_prod_map_map","ProbabilityTheory.iIndepFun","ProbabilityTheory.iIndepFun.indepFun","ProbabilityTheory.iIndepFun_iff_map_fun_eq_pi_map","Prod","Prod.instMeasurableSpace","Prod.mk","congrArg","funext","id","measurable_pi_apply","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CollisionNull","name":"_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.measure_prod_diagonal_eq_zero","type_dependencies":["DFunLike.coe","ENNReal","ENNReal.instZero","Eq","MeasurableEq","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.prod","MeasureTheory.NullSingletonClass","MeasureTheory.SFinite","OfNat.ofNat","Prod","Prod.instMeasurableSpace","Set","Set.diagonal","Zero.toOfNat0"],"value_dependencies":["DFunLike.coe","ENNReal","ENNReal.instZero","Eq","Eq.mpr","Eq.trans","Filter.EventuallyEq","Filter.univ_mem'","MeasurableEq","MeasurableEq.measurableSet_diagonal","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.measure_prod_null","MeasureTheory.Measure.prod","MeasureTheory.NullSingletonClass","MeasureTheory.NullSingletonClass.measure_singleton","MeasureTheory.SFinite","MeasureTheory.ae","Membership.mem","OfNat.ofNat","Pi.instZero","Prod","Prod.instMeasurableSpace","Prod.mk","Set","Set.diagonal","Set.instMembership","Set.instSingletonSet","Set.ofPred","Set.ofPred_eq_eq_singleton'","Set.preimage","Singleton.singleton","True","Zero.toOfNat0","congrArg","congrFun'","eq_self","id","of_eq_true","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CollisionNull","name":"_private.GinibrePoincare.Analysis.CollisionNull.0.GinibrePoincare.vandermondeDensity_ne_zero_ae._simp_1_1","type_dependencies":["Eq","Not"],"value_dependencies":["Classical.not_not","Not","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CompactLipschitzLSIExtension","name":"_private.GinibrePoincare.Analysis.CompactLipschitzLSIExtension.0.GinibrePoincare.directionalEnergy_bound","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.hasOpNorm","DenselyNormedField.toNontriviallyNormedField","Field.toSemifield","Finset.sum","Finset.univ","Fintype","GinibrePoincare.directionalEnergy","HMul.hMul","HPow.hPow","InnerProductSpace.toNormedSpace","LE.le","Monoid.toNPow","NNReal","NNReal.toReal","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instRCLike","Real.norm","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instHPow","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.hasOpNorm","ContinuousLinearMap.le_opNorm","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Finset","Finset.instSetLike","Finset.sum","Finset.sum_le_sum","Finset.sum_nonneg","Finset.univ","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.swap","GinibrePoincare.directionalEnergy","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_lt_of_eq","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NNReal","NNReal.toReal","NPow.toPow","Nat","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddLeftCancelSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRCLike","Real.instRing","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.norm_eq_abs","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","RingHomIsometric.ids","Semifield.toCommSemiring","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","abs","abs_nonneg","abs_of_nonneg","addRightReflectLE_of_addLeftReflectLE","congrArg","contravariant_lt_of_covariant_le","fderiv","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instIsRightCancelAddOfAddRightReflectLE","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","mul_le_mul_of_nonneg_right","mul_nonneg_of_nonpos_of_nonpos","neg_eq_zero","norm_nonneg","rfl","sq_abs","sq_nonneg","sub_eq_zero_of_eq"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CompactLipschitzLSIExtension","name":"_private.GinibrePoincare.Analysis.CompactLipschitzLSIExtension.0.GinibrePoincare.norm_mollification_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.normed","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","InnerProductSpace.toNormedSpace","IsScalarTower.right","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.convolution","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instDivisionRing","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","BorelSpace.opensMeasurable","CommSemiring.toSemiring","ContDiff.continuous","ContDiffBump","ContDiffBump.contDiff_normed","ContDiffBump.hasCompactSupport_normed","ContDiffBump.integral_normed","ContDiffBump.nonneg_normed","ContDiffBump.normed","Continuous.integrable_of_hasCompactSupport","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","ENat","Eq","Eq.mpr","Eq.refl","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually.of_forall","FiniteDimensional","FiniteDimensional.proper_real","HMul.hMul","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","LE.le","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_const","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.integral","MeasureTheory.integral_mono_of_nonneg","MeasureTheory.integral_mul_const","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.norm_integral_le_integral_norm","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toSMulWithZero","MulZeroOneClass.toMulOneClass","NegZeroClass.toZero","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instZero","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","Trans.trans","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","abs","abs_of_nonneg","congrArg","id","instClosedIciTopology","instDistribOfSemiring","instHMul","instHSMul","instHSub","instHasSolidNormReal","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instSMulOfMul","instTopENat","instTransEq_1","instTransLE","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","mul_le_mul_of_nonneg_left","norm_nonneg","norm_smul","one_mul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianDensity","name":"_private.GinibrePoincare.Analysis.ComplexGaussianDensity.0.GinibrePoincare.coordinate_density_product_formula","type_dependencies":["CommSemiring.toCommMonoid","ENNReal","ENNReal.instCommSemiring","Eq","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianDensity","GinibrePoincare.complexGaussianDensity","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dependencies":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toCommMonoid","Complex","Complex.instSemiring","Complex.normSq","DFunLike.coe","Distrib.toMul","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instCommSemiring","ENNReal.ofReal","ENNReal.ofReal_prod_of_nonneg","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.instSetLike","Finset.mul_sum","Finset.prod","Finset.prod_const","Finset.prod_mul_distrib","Finset.sum","Finset.univ","Fintype.card_fin","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.complexCoordinateGaussianDensity","GinibrePoincare.complexGaussianDensity","GinibrePoincare.gaussianWeight","HDiv.hDiv","HMul.hMul","HPow.hPow","HasDistribNeg.toInvolutiveNeg","Iff.mpr","InvolutiveNeg.toNeg","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toPosMulStrictMono","LT.lt","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast","Nat.cast_pos'","NeZero.charZero_one","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","Real","Real.commRing","Real.exp","Real.exp_pos","Real.exp_sum","Real.instAddCommMonoid","Real.instCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.pi","Real.pi_pos","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SetLike.instMembership","True","Zero.toOfNat0","congr","congrArg","div_pos","eq_self","id","instHDiv","instHMul","instHPow","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","le_of_lt","mul_pos","neg_mul","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.ComplexGaussianDensity","name":"_private.GinibrePoincare.Analysis.ComplexGaussianDensity.0.GinibrePoincare.real_density_product_formula","type_dependencies":["CommSemiring.toCommMonoid","Complex","Complex.measurableEquivPi","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instCommSemiring","Eq","EquivLike.toFunLike","Fin","Fin.fintype","Finset.prod","Finset.univ","GinibrePoincare.complexCoordinateGaussianDensity","GinibrePoincare.realCoordinateVariance","LT.lt","MeasurableEquiv","MeasurableEquiv.instEquivLike","MeasurableEquiv.symm","MeasurableSpace.pi","Nat","OfNat.ofNat","ProbabilityTheory.gaussianPDF","Real","Real.instZero","Real.measurableSpace","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.I","Complex.im","Complex.instAdd","Complex.instMul","Complex.measurableEquivPi","Complex.measurableSpace","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMo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rePoincare.cauchyGreenRegularizedKernel_dbar._simp_1_8","type_dependencies":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dependencies":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenRegularized","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenRegularized.0.GinibrePoincare.cauchyGreenRegularizedKernel_dbar._simp_1_9","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenRegularized","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenRegularized.0.GinibrePoincare.normSq_hasFDerivAt","type_dependencies":["Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HasFDerivAt","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","MonoidWithZeroHom","MonoidWithZeroHom.funLike","MulZeroClass.toMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMul","Real.instNatCast","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","UniformSpace.toTopologicalSpace","instHAdd","instHMul","instHSMul","instIsTopologicalRingReal","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Algebra.id","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.im","Complex.imCLM","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.normSq_apply","Complex.re","Complex.reCLM","ContinuousLinearMap","ContinuousLinearMap.add","ContinuousLinearMap.ext","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.instIsAddApply","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","HAdd.hAdd","HEq","HEq.casesOn","HEq.refl","HMul.hMul","HPow.hPow","HSMul.hSMul","HasFDerivAt","HasFDerivAt.add","HasFDerivAt.mul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormN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opologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Min.min","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteGramSchmidt.0.GinibrePoincare.hermiteScale","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteGramSchmidt.0.GinibrePoincare.rawScalar","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteGramSchmidt.0.GinibrePoincare.singleHermite","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteGramSchmidt.0.GinibrePoincare.singleMonomial","instAddNat","instHAdd","instHSMul","instHSub","instMinNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","Complex.ofReal","ContinuousENorm.toENorm","DFunLike.coe","Decidable.decide","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.trans","Field.toDivisionRing","Field.toSemifield","Filter.Eventually","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Fin.fintype","Fin.instOfNat","Fin.prod_univ_one","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.range","Finset.sum","Finset.sum_congr","Finset.univ","Function.hasSMul","GinibrePoincare.ComplexHermite.multivariateNormalized","GinibrePoincare.ComplexHermite.normalizedEval","GinibrePoincare.ComplexHermite.normalizedEval_eq_sum","GinibrePoincare.ComplexHermite.oneDimNormalization","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.memLp_two_multivariateMixedMonomial","GinibrePoincare.multivariateMixedMonomialL2._proof_1","GinibrePoincare.multivariateNormalizedL2","GinibrePoincare.multivariateNormalizedL2_coeFn","HAdd.hAdd","HMul","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","InvOneClass.toOne","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_fun_finsetSum","MeasureTheory.Lp.coeFn_smul","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","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ountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Eventually.of_forall","Filter.instMembership","Fin","Fin.fintype","GinibrePoincare.Configuration","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.continuous_convolution_left","HasCompactSupport.convolutionExists_left","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasurableSpace.pi","MeasureTheory.ConvolutionExists","MeasureTheory.ConvolutionExistsAt","MeasureTheory.Integrable.norm","MeasureTheory.IntegrableAtFilter","MeasureTheory.IntegrableOn","MeasureTheory.IsAddLeftInvariant.isAddRightInvariant","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.aestronglyMeasurable","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instIsAddRightInvariantForallVolumeOfMeasurableAddOfSigmaFinite","MeasureTheory.Measure.instIsLocallyFiniteMeasureForallVolumeOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.instSigmaFiniteForallVolume","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.Pi.isAddLeftInvariant_volume","MeasureTheory.Pi.isNegInvariant_volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.convolution_assoc","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","Pi.addCommGroup","Pi.addGroup","Pi.borelSpace","Pi.instSub","Pi.isTopologicalAddGroup","Pi.measurableAdd\u2082","Pi.measurableNeg","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instCompleteSpace","Real.instMonoid","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.IsCompletelyPseudoMetrizableSpace.of_completeSpace_pseudometrizable","TopologicalSpace.SecondCountableTopology.to_separableSpace","TopologicalSpace.instSecondCountableTopologyForallOfCountable","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instCountableFin","instDistribOfSemiring","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instSecondCountableTopologyReal","instSeparatelyContinuousAddOfContinuousAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","norm_zero","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointWeyl","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointWeyl.0.GinibrePoincare.configuration_real_kernel_convolution_comm","type_dependencies":["Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instSub","Complex.measurableSpace","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","Pi.instSub","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.measurableSpace","ContinuousAdd.measurableAdd","ContinuousLinearMap.lsmul","ContinuousNeg.measurableNeg","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetric.instIsCountablyGeneratedUniformity","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","Fin","Fin.fintype","GinibrePoincare.Configuration","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.Measure","MeasureTheory.Measure.InnerRegularCompactLTTop.instInnerRegularOfSigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.Pi.isAddLeftInvariant_volume","MeasureTheory.Pi.isNegInvariant_volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.convolution_lsmul","MeasureTheory.convolution_lsmul_swap","MeasureTheory.instInnerRegularCompactLTTopOfIsCompletelyPseudoMetrizableSpace","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Nat","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNon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AuxiliaryLocalDolbeaultBoundaryIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundaryIteration.0.GinibrePoincare.smoothDolbeaultPrimitive.match_1.splitter","type_dependencies":["Fin","List","List.cons","List.nil","Nat","Unit"],"value_dependencies":["GinibrePoincare.smoothDolbeaultPrimitive.match_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultInterior","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultInterior.0.GinibrePoincare.dolbeaultBump_translated_tsupport._simp_1_1","type_dependencies":["Dist.dist","Eq","LT.lt","Membership.mem","Metric.ball","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLT","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LT.lt","Membership.mem","Metric.ball","Metric.mem_ball","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLT","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpBall","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpBall.0.GinibrePoincare.localDolbeault_compactLp_ball._simp_1_1","type_dependencies":["Dist.dist","Eq","LT.lt","Membership.mem","Metric.ball","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLT","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LT.lt","Membership.mem","Metric.ball","Metric.mem_ball","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLT","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpBall","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpBall.0.GinibrePoincare.localDolbeault_compactLp_ball._simp_1_2","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration.0.GinibrePoincare.dolbeaultBoundaryLpComposition.match_1.eq_1","type_dependencies":["Eq","Fin","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","List","List.cons","List.nil","Nat","Unit","Unit.unit"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","List","List.cons","List.nil","Nat","Unit"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration.0.GinibrePoincare.dolbeaultBoundaryLpComposition.match_1.eq_2","type_dependencies":["Eq","Fin","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","List","List.cons","List.nil","Nat","Unit"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.dolbeaultBoundaryLpComposition.match_1","List","List.cons","List.nil","Nat","Unit"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration.0.GinibrePoincare.dolbeaultBoundaryLpComposition.match_1.splitter","type_dependencies":["Fin","List","List.cons","List.nil","Nat","Unit"],"value_dependencies":["GinibrePoincare.dolbeaultBoundaryLpComposition.match_1"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration.0.GinibrePoincare.truncatedDolbeaultPrimitive.match_1.eq_1","type_dependencies":["Eq","Fin","GinibrePoincare.truncatedDolbeaultPrimitive.match_1","List","List.cons","List.nil","Nat","Unit","Unit.unit"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.truncatedDolbeaultPrimitive.match_1","List","List.cons","List.nil","Nat","Unit"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration.0.GinibrePoincare.truncatedDolbeaultPrimitive.match_1.eq_2","type_dependencies":["Eq","Fin","GinibrePoincare.truncatedDolbeaultPrimitive.match_1","List","List.cons","List.nil","Nat","Unit"],"value_dependencies":["Eq.refl","Fin","GinibrePoincare.truncatedDolbeaultPrimitive.match_1","List","List.cons","List.nil","Nat","Unit"]},{"kind":"definition","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxil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at","Ne","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PartialOrder.toPreorder","Pi.topologicalSpace","Preorder.toLT","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.instLT","Real.instPreorder","Real.instZero","Real.measurableSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff._simp_1","Singleton.singleton","True","UniformSpace.toTopologicalSpace","Zero.toOfNat0","eq_self","instInnerProductSpaceRealComplex","isCompact_singleton","measureSpaceOfInnerProductSpace","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightUniform","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightUniform.0.GinibrePoincare.kernel_bound","type_dependencies":["And","Exists","GinibrePoincare.Configuration","GinibrePoincare.configurationRadialSmoothingKernel","LE.le","Nat","Norm.norm","OfNat.ofNat","Real","Real.instLE","Real.instZero","Real.norm","Zero.toOfNat0"],"value_dependencies":["AddGroup.toSubtractionMonoid","And","And.intro","BddAbove","Classical.propDecidable","Complex","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff.continuous","Continuous.continuousOn","Continuous.norm","DenselyNormedField.toNontriviallyNormedField","DistribLattice.toLattice","ENat","Eq","Eq.mpr","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationRadialSmoothingKernel","GinibrePoincare.configurationRadialSmoothingKernel_compact","GinibrePoincare.configurationRadialSmoothingKernel_contDiff","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsCompact.bddAbove_image","LE.le","LE.le.trans","Lattice.toSemilatticeInf","Max.max","Membership.mem","Nat","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","Norm.norm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instInhabited","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMax","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.pseudoMetricSpace","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toAddGroup","SeminormedAddGroup.toNorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.image","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","congrArg","dite","id","image_eq_zero_of_notMem_tsupport","instClosedIciTopology","instDistribLatticeOfLinearOrder","instHasSolidNormReal","instInnerProductSpaceRealComplex","instNonemptyOfInhabited","instTopENat","le_max_left","le_max_right","norm_zero","rfl","tsupport","upperBounds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightUniform","name":"_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightUniform.0.GinibrePoincare.kernel_support_ball","type_dependencies":["Complex","Complex.instNormedField","Complex.instZero","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationRadialSmoothingKernel","LE.le","Metric.closedBall","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instZero","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instNatCast","Real.instZero","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instLE","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instOfNatAtLeastTwo","instOfNatNat","pseudoMetricSpacePi","tsupport"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Bool","Bool.false","Bool.true","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField",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oid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.DegreeHermiteIndex","GinibrePoincare.DegreeHermiteIndex.val","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.instLinearOrderDegreeHermiteIndex","GinibrePoincare.tensorHermiteScale","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","Inv.inv","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Lattice.toSemilatticeInf","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PartialOrder.toPreorder","Prod.fst","Prod.snd","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Ring.toSemiring","SMulZeroClass.toSMul","SemilatticeInf.toPartialOrder","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Set.Iio","Set.image","SetLike.instMembership","Submodule","Submodule.setLike","Submodule.span","Subtype","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryTensorGramSchmidt.0.GinibrePoincare.degreeHermiteFamily","_private.GinibrePoincare.Analysis.CorrespondenceAuxiliaryTensorGramSchmidt.0.GinibrePoincare.degreeMonomialFamily","instDistribLatticeOfLinearOrder","instHSMul","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.left","CommMonoid.toMonoid","CommRing.toCommMonoid","Complex","Complex.addGroupWithOne","Complex.commRing","Complex.instAddCommMonoid","Complex.instField","Complex.instInv","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_ne_zero","DistribLattice.toLattice","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","DivisionSemiring.toGroupWithZero","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","Field.toSemifield","Fin","Fin.fintype","Fin.val","Finset","Finset.add_sum_erase","Finset.erase","Finset.instSetLike","Finset.mem_erase","Finset.mem_univ","Finset.mem_univ._simp_1","Finset.prod","Finset.prod_congr","Finset.prod_const_one","Finset.sum","Finset.sum_congr","Finset.sum_erase_eq_sub","Finset.univ","Fintype.decidablePiFintype","GinibrePoincare.Configuration","GinibrePoincare.DegreeHermiteIndex","GinibrePoincare.DegreeHermiteIndex.mk","GinibrePoincare.D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rePoincare.Configuration","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibreMeasure_isProbabilityMeasure","HMul.hMul","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","Iff.mpr","InnerProductSpace.toNormedSpace","Inter.inter","IsClosed.measurableSet","IsCompact","IsCompact.measurableSet","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","IsTopologicalAddGroup.to_continuousSub","LE","LE.le","LT.lt","LinearOrder.toPartialOrder","MeasurableSet","MeasurableSet.inter","MeasurableSet.univ._simp_1","MeasurableSpace.pi","MeasureTheory.Integrable","MeasureTheory.Integrable.indicator","MeasureTheory.IntegrableOn","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.real","MeasureTheory.Measure.restrict","MeasureTheory.Measure.restrict_apply","MeasureTheory.ae","MeasureTheory.ae_restrict_mem","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MeasureTheory.integral","MeasureTheory.integral_const","MeasureTheory.integral_indicator","MeasureTheory.integral_mono_ae","MeasureTheory.isFiniteMeasureRestrict","Membership.mem","Module.toDistribMulAction","MulZeroClass.toSMulWithZero","Nat","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toENormedAddCommMonoid","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Not","OfNat.ofNat","PartialOrder.toPreorder","Pi.opensMeasurableSpace","Pi.t2Space","Pi.topologicalSpace","Preorder.toLE","Preorder.toLT","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.decidableLE","Real.instCompleteSpace","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instPreorder","Real.instRCLike","Real.instZero","Real.lattice","Real.linearOrder","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.decidableSetOf","Set.indicator","Set.indicator_of_mem","Set.indicator_of_notMem","Set.instInter","Set.instLE","Set.instMembership","Set.inter_eq_left","Set.ofPred","Set.univ","Set.univ_inter","Std.le_refl._simp_1","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformSpace.toTopologicalSpace","Zero","Zero.toOfNat0","congr","congrArg","congrFun'","continuous_apply","continuous_const","dite","eq_true","ge_iff_le._simp_1","id","instClosedIciTopology","instCountableFin","instDecidableAnd","instHMul","instHSMul","instHSub","instHasSolidNormReal","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","instReflLe","isClosed_le","lt_of_not_ge","mul_comm","not_le._simp_1","of_eq_true","secondCountable_of_proper","true_and"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCollisionRates","name":"_private.GinibrePoincare.Analysis.CorrespondenceCollisionRates.0.GinibrePoincare.correspondenceCollisionCutoff_compact_rates._simp_1_1","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","two_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCollisionRates","name":"_private.GinibrePoincare.Analysis.CorrespondenceCollisionRates.0.GinibrePoincare.correspondenceCollisionCutoff_compact_rates._simp_1_2","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","three_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceCollisionRates","name":"_private.GinibrePoincare.Analysis.CorrespondenceCollisionRates.0.GinibrePoincare.correspondenceCollisionCutoff_compact_rates._simp_1_3","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNa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LebesgueDensityReal","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instHMul","instInnerProductSpaceRealComplex"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorGreen","name":"_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityFlux.eq_1","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Eq","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreLebesgueDensityReal","HMul.hMul","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityFlux","fderiv","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["Eq.refl","GinibrePoincare.Configuration","Nat","Real","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityFlux"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.CorrespondenceOperatorGreen","name":"_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_derivative_greenFlux","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","HMul.hMul","HSub.hSub","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instMul","Real.instRCLike","Real.instSub","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityFlux","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_greenFlux","fderiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instTopENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.to_smulCommClass","CommRing.toCommSemiring","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemir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ormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.instSetLike","Finset.mul_sum","Finset.sum","Finset.sum_congr","Finset.univ","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.Configuration","GinibrePoincare.imaginaryCoordinateDirection","GinibrePoincare.realCoordinateDirection","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.RingNF.add_assoc_rev","Mathlib.Tactic.RingNF.add_neg","Mathlib.Tactic.RingNF.int_rawCast_neg","Mathlib.Tactic.RingNF.mul_assoc_rev","Mathlib.Tactic.RingNF.mul_neg","Mathlib.Tactic.RingNF.nat_rawCast_1","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_one","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRCLike","Real.instRing","Real.instSub","Real.linearOrder","Real.normedAddCommGroup","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityDivergence","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_densityFlux","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.GinibrePoincare.correspondenceOperator_derivative_greenFlux","_private.GinibrePoincare.Analysis.CorrespondenceOperatorGreen.0.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ormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","Real","Real.instDivisionRing","Real.normedField","instOfNatNat"],"value_dependencies":["FiniteDimensional.rclike_to_real","Real","Real.instRCLike"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instFiniteDimensionalRealGaussianProductSpace._proof_2","type_dependencies":["FiniteDimensional","GinibrePoincare.GaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","HAdd.hAdd","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","Real","Real.instDivisionRing","Real.normedField","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","DivisionRing.toRing","FiniteDimensional","GinibrePoincare.GaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","IsSimpleModule.instIsNoetherian","Module.IsNoetherian.finite","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","Prod","Prod.instAddCommGroup","Prod.instModule","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instDivisionRing","Real.instRing","Real.normedField","Ring.toSemiring","Semiring.toModule","instIsSimpleModule","isNoetherian_of_isNoetherianRing_of_finite","isNoetherian_prod"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instIsAddHaarMeasureGaussianProductSpaceGaussianProductHaar._proof_1","type_dependencies":["AddCommGroup.toAddGroup","GinibrePoincare.GaussianProductSpace","GinibrePoincare.gaussianProductHaar","GinibrePoincare.instMeasurableSpaceGaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","MeasureTheory.Measure.IsAddHaarMeasure","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instOfNatNat"],"value_dependencies":["FiniteDimensional.rclike_to_real","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.instRCLike","Real.measurableSpace","Real.normedAddCommGroup","instIsAddHaarMeasureVolume"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GaussianLSIFiniteProduct","name":"_private.GinibrePoincare.Analysis.GaussianLSIFiniteProduct.0.GinibrePoincare.instIsAddHaarMeasureGaussianProductSpaceGaussianProductHaar._proof_2","type_dependencies":["AddCommGroup.toAddGroup","GinibrePoincare.GaussianProductSpace","GinibrePoincare.gaussianProductHaar","GinibrePoincare.instMeasurableSpaceGaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","HAdd.hAdd","MeasureTheory.Measure.IsAddHaarMeasure","Nat","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","instAddNat","instHAdd","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","ContinuousAdd.measurableAdd","FiniteDimensional.proper_real","FiniteDimensional.rclike_to_real","GinibrePoincare.GaussianProductSpace","GinibrePoincare.gaussianProductHaar","GinibrePoincare.instBorelSpaceGaussianProductSpace","GinibrePoincare.instFiniteDimensionalRealGaussianProductSpace","GinibrePoincare.instMeasurableSpaceGaussianProductSpace","GinibrePoincare.instNormedAddCommGroupGaussianProductSpace","GinibrePoincare.instNormedSpaceRealGaussianProductSpace","GinibrePoincare.instSecondCountableTopologyGaussianProductSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.prod.instIsAddHaarMeasure","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.borelSpace","Real.commRing","Real.instAd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uousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Field.toDivisionRing","Fin","Fin.fintype","Fin.instLinearOrderPackage","Fin.instPartialOrder","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.complexSuccessiveProjections","GinibrePoincare.l2PiProductVector","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPiBergmanCoordinate","HAdd.hAdd","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","List","List.Nodup","List.instDecidableMemOfLawfulBEq","List.instMembership","List.map","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.pi","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","SetLike.instMembership","Std.LinearOrderPackage.toLinearPreorderPackage","Std.LinearPreorderPackage.toPreorderPackage","Std.PreorderPackage.toBEq","Std.PreorderPackage.toLawfulOrderBEq","Std.instLawfulBEqOfLawfulOrderBEqOfIsPartialOrder","Subtype","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fact_one_le_two_ennreal","instAddNat","instHAdd","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instIsPartialOrder_mathlib","instLEFin","instOfNatAtLeastTwo","instOfNatNat","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","ite","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","secondCountable_of_proper"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","And","And.left","And.right","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContDiff","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.id","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Field.toDivisionRing","Fin","Fin.fintype","Fin.instLinearOrderPackage","Fin.instPartialOrder","Function.update","Function.update_congr","Function.update_self","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2","GinibrePoincare.PlanarPiLebesgueL2._proof_1","GinibrePoincare.Potential","GinibrePoincare.complexSuccessiveProjections","GinibrePoincare.complexSuccessiveProjections._proof_1","GinibrePoincare.l2PiCoordinateOperator","GinibrePoincare.l2PiCoordinateOperator_pure","GinibrePoincare.l2PiProductVector","GinibrePoincare.l2PiProductVector.congr_simp","GinibrePoincare.planarBergmanProjection","GinibrePoincare.planarCompactTestSpace._proof_2","Ginibre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CommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHAdd","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.sub","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddZeroClass","CStarRing.to_normedStarGroup","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreHolomorphicAmbientClosedSpan","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","SubNegZeroMonoid.toNegZeroClass","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","add_zero","fact_one_le_two_ennreal","instDistribOfSemiring","instHAdd","instHSub","instLTNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreComplexProjectionGeometry","name":"_private.GinibrePoincare.Analysis.GinibreComplexProjectionGeometry.0.GinibrePoincare.projection_inner_of_mem","type_dependencies":["AddCommGroup.toAddCommMonoid","ClosedSubmodule","ClosedSubmodule.instSetLike","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","Eq","Field.toSemifield","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Membership.mem","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","ClosedSubmodule","ClosedSubmodule.instSetLike","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","CompleteSpace","Complex","Complex.addGroupWithOne","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","DivisionRing.toRing","Eq","Eq.mp","Eq.symm","Field.toDivisionRing","Field.toSemifield","HSub.hSub","Iff.mp","Inner.inner","InnerProductSpace","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","Membership.mem","MulZeroClass.toZero","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","Ring.toAddGroupWithOne","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","Submodule.starProjection_inner_eq_zero","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","inner_sub_left","instHSub","instMulZeroClassOfSemiring","sub_eq_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"_private.GinibrePoincare.Analysis.GinibreConjugationGeometry.0.GinibrePoincare.Lp_norm_star","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","Real","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","ContinuousENorm.toENorm","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.toReal","Eq","Eq.mpr","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.eLpNorm_star","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instNorm","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Lp.norm_def","MeasureTheory.eLpNorm","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","Real","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","id","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"_private.GinibrePoincare.Analysis.GinibreConjugationGeometry.0.GinibrePoincare.Lp_star_add","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HAdd.hAdd","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","AddSubgroup","AddSubgroup.add","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAdd","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Filter.mp_mem","Filter.univ_mem'","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HAdd.hAdd","InvolutiveStar.toStar","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_add","MeasureTheory.Lp.coeFn_star","MeasureTheory.Lp.ext","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toField","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instAdd","Pi.instStarForall","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","RCLike.toDenselyNormedField","RCLike.toStarRing","RingHom","RingHom.instFunLike","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.star_add","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","Trans.trans","True","UniformSpace.toTopologicalSpace","congrArg","congrArg\u2082","congrFun'","eq_self","id","instHAdd","instOfNatAtLeastTwo","instOfNatNat","instTransEq","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"_private.GinibrePoincare.Analysis.GinibreConjugationGeometry.0.GinibrePoincare.Lp_star_real_smul","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarRing.to_normedStarGroup","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.instCStarRing","Real","Real.instMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Algebra.toSMul","CStarRing.to_normedStarGroup","CommMagma.toMul","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.conj_ofReal","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DenselyNormedField.toNormedField","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroCl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omplex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Eq.refl","Filter.EventuallyEq","Filter.mp_mem","Filter.univ_mem'","Fin","Function.comp","GinibrePoincare.Configuration","GinibrePoincare.ParticlePermutation","GinibrePoincare.ginibreMeasure","GinibrePoincare.ginibrePermutationL2","GinibrePoincare.ginibre_measurePreserving_permute","GinibrePoincare.permute","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsTopologicalAddGroup.toContinuousAdd","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.coeFn_compMeasurePreserving","MeasureTheory.Lp.coeFn_star","MeasureTheory.Lp.compMeasurePreserving","MeasureTheory.Lp.ext","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","MeasureTheory.Measure","MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq_comp","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasurePreserving.quasiMeasurePreserving","MeasureTheory.ae","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.instStarForall","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","congrArg","fact_one_le_two_ennreal","id","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreConjugationGeometry","name":"_private.GinibrePoincare.Analysis.GinibreConjugationGeometry.0.GinibrePoincare.inner_Lp_star_star","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instStarRing","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","Inner.inner","InvolutiveStar.toStar","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","CStarRing.to_normedStarGroup","CommMagma.toMul","CommSemiring.toSemiring","Complex","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.i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b.hSub","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.instZero","Real.measureSpace","Real.normedField","SubNegMonoid.toSub","Zero.toOfNat0","instHAdd","instHSub","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.instZero","Real.measureSpace","Real.normedField","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHSub","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathLocalExistence","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathLocalExistence.0.GinibrePoincare.ginibreDrivenPath_continuous_noise_local_exists._abel_1_2","type_dependencies":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","HAdd.hAdd","HSub.hSub","Nat","NormedAddCommGroup.toAddCommGroup","Pi.instAdd","Pi.normedAddCommGroup","Real","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instZero","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","GinibrePoincare.Configuration","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","Nat","Neg.neg","NegZeroClass.toNeg","NormedAddCommGroup.toAddCommGroup","OfNat.ofNat","Pi.addCommGroup","Pi.addZeroClass","Pi.instAdd","Pi.instNeg","Pi.instZero","Pi.negZeroClass","Pi.normedAddCommGroup","Pi.subtractionMonoid","Real","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSub","instOfNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathLocalExistence","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathLocalExistence.0.GinibrePoincare.ginibreDrivenPath_continuous_noise_local_exists._simp_1_1","type_dependencies":["Complex","Complex.instZero","Eq","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","Nat","Ne","OfNat.ofNat","Zero.toOfNat0"],"value_dependencies":["Complex","Complex.instZero","Eq.symm","GinibrePoincare.CollisionFree","GinibrePoincare.Configuration","GinibrePoincare.vandermonde","GinibrePoincare.vandermonde_ne_zero_iff","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOU","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathOU.0.GinibrePoincare.drivenOUPath_integral_equation._abel_1_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","Eq","GinibrePoincare.drivenOUCorrection","HAdd.hAdd","HSub.hSub","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","Real","Real.normedField","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.drivenOUCorrection","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","OfNat.ofNat","Real","Real.normedField","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSub","instOfNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOU","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathOU.0.GinibrePoincare.drivenOUPath_unique._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Zero.toOfNat0","instHAdd","instHSMul","instHSub","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHSMul","instHSub","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUShift","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathOUShift.0.GinibrePoincare.drivenOUPath_initial_split._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHMul","instHSMul","instHSub","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","Int","Int.instNegInt","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.exp","Real.instMonoid","Real.instMul","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHMul","instHSMul","instHSub","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUShift","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathOUShift.0.GinibrePoincare.drivenOUPath_shift._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instAdd","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Zero.toOfNat0","instHAdd","instHSMul","instHSub","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instAdd","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSMul","instHSub","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathOUUniqueness","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathOUUniqueness.0.GinibrePoincare.drivenOUPath_unique_nonneg._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Zero.toOfNat0","instHAdd","instHSMul","instHSub","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.refl","Eq.symm","Eq.trans","GinibrePoincare.drivenOUPath","HAdd.hAdd","HSMul.hSMul","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instNeg","Real.instZero","Real.measureSpace","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instDistribOfSemiring","instHAdd","instHSMul","instHSub","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRestart","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathRestart.0.GinibrePoincare.ginibreDrivenPath_shift._abel_1_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.ginibreLangevinDrift","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.to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le.toDistribMulAction","Nat","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instRing","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instAddNat","instDistribOfSemiring","instHAdd","instHSMul","instHSub","instOfNat","instOfNatNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathRiemann","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathRiemann.0.GinibrePoincare.ginibreWeightedIncrements_integral_error._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","Finset.range","Finset.sum","HAdd.hAdd","HSMul.hSMul","HSub.hSub","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Nat","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instSub","Real.measureSpace","Real.normedField","Real.semiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instAddNat","instHAdd","instHSMul","instHSub","instOfNatNat","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toAdd","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.refl","Eq.symm","Eq.trans","Finset.range","Finset.sum","HAdd.hAdd","HSMul.hSMul","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Module.toDistribMulAction","Nat","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace","NormedSpace.toModule","OfNat.ofNat","Real","Real.instMonoid","Real.instSub","Real.measureSpace","Real.normedField","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SMulZeroClass.toSMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instAddNat","instDistribOfSemiring","instHAdd","instHSMul","instHSub","instOfNat","instOfNatNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence.0.GinibrePoincare.drivenContinuousNoise_lipschitz_uniform_local._abel_1_2","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","Eq","HAdd.hAdd","HSub.hSub","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","Real","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instNegInt","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","OfNat.ofNat","Real","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instHAdd","instHSub","instOfNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence.0.GinibrePoincare.drivenContinuousNoise_lipschitz_uniform_local._abel_1_3","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","Eq","HAdd.hAdd","HSub.hSub","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","Real","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","OfNat.ofNat","Real","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSub","instOfNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence.0.GinibrePoincare.drivenContinuousNoise_lipschitz_uniform_local._simp_1_1","type_dependencies":["Dist.dist","Eq","LE.le","Membership.mem","Metric.closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership"],"value_dependencies":["Dist.dist","LE.le","Membership.mem","Metric.closedBall","Metric.mem_closedBall","PseudoMetricSpace","PseudoMetricSpace.toDist","Real","Real.instLE","Set","Set.instMembership","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness.0.GinibrePoincare.ginibreDrivenPath_local_pathwise_unique._abel_1_1","type_dependencies":["Complex","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Eq","Fin","Fin.fintype","GinibrePoincare.Configuration","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instAdd","Pi.instSub","Pi.normedAddCommGroup","Pi.normedSpace","Real","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","SeminormedCommRing.toNonUnitalSeminormedCommRing","Zero.toOfNat0","instHAdd","instHSub","instInnerProductSpaceRealComplex","intervalIntegral"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAdd","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","GinibrePoincare.Configuration","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasureTheory.MeasureSpace.volume","Nat","Neg.neg","NegZeroClass.toNeg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.addCommGroup","Pi.addZeroClass","Pi.instAdd","Pi.instNeg","Pi.instZero","Pi.negZeroClass","Pi.normedAddCommGroup","Pi.normedSpace","Pi.subtractionMonoid","Real","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedField","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSub","instInnerProductSpaceRealComplex","instOfNat","intervalIntegral","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness","name":"_private.GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness.0.GinibrePoincare.ginibreDrivenPath_local_pathwise_unique._simp_1_3","type_dependencies":["AddGroup","AddGroup.toSubNegMonoid","Eq","HSub.hSub","SubNegMonoid.toSub","instHSub"],"value_dependencies":["AddGroup","AddGroup.toSubNegMonoid","Eq","HSub.hSub","SubNegMonoid.toSub","instHSub","propext","sub_left_inj"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreDynamicsDrift","name":"_private.GinibrePoincare.Analysis.GinibreDynamicsDrift.0.GinibrePoincare.coordinateSum_ginibreCoulombInteraction._simp_1_1","type_dependencies":["Eq","Finset","Finset.sum","Neg.neg","NegZeroClass.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid"],"value_dependencies":["Eq.symm","Finset","Finset.sum","Finset.sum_neg_distrib","Neg.neg","NegZeroClass.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionBridge","name":"_private.GinibrePoincare.Analysis.GinibreEntireProjectionBridge.0.GinibrePoincare.ginibreDivisibleEntire_exists_symmetricRepresentative._simp_1_1","type_dependencies":["Eq","Not"],"value_dependencies":["Classical.not_not","Not","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEntireProjectionDistance","name":"_private.GinibrePoincare.Analysis.GinibreEntireProjectionDistance.0.GinibrePoincare.ginibreHolomorphicDistanceSq_eq_projectionNorm._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousENorm.toENorm","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreDivisibleEntireClosedSpace","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.MemLp","MeasureTheory.MemL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_simp_1_8","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"_private.GinibrePoincare.Analysis.GinibreEqualityConjugateProjection.0.GinibrePoincare.conjugateAntiMode_complex_smul","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toNormedRing","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.ginibreFullConjugateAntiMode","GinibrePoincare.ginibreMeasure","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoi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Mul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Module.toDistribMulAction","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","Real","Real.instOne","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.continuousSemilinearMapClass","ContinuousLinearMap.funLike","ContinuousSemilinearMapClass.toSemilinearMapClass","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.trans","Field.toDivisionRing","Fin","GinibrePoincare.ComplexHermite.hermiteAntiDegreeProjection","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.gaussianGlobalPhaseL2","GinibrePoincare.gaussianGlobalPhaseL2_comm_antiDegreeProjection","GinibrePoincare.gaussianGlobalPhaseL2_normalizedVandermonde_character","GinibrePoincare.ginibreFullConjugateAntiMode","GinibrePoincare.ginibreGlobalPhaseL2","GinibrePoincare.ginibreGlobalPhaseL2_star_eigen","GinibrePoincare.ginibreMeasure","GinibrePoincare.normalizedVandermondeL2","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HMul.hMul","HPow.hPow","HSMul.hSMul","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","LinearIsometry","LinearIsometry.instFunLike","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZeroHomClass.toMonoidHomClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toMulZeroOneClass","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.instCStarRing","Real","Real.instOne","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.semiring","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","RingHom.instRingHomClass","RingHomClass.toMonoidWithZeroHomClass","SMulZeroClass.toSMul","SemilinearMapClass.toMulActionSemiHomClass","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","congrArg","congrFun'","fact_one_le_two_ennreal","id","instAddNat","instCommCStarAlgebraComplex","instHAdd","instHMul","instHPow","instHSMul","instInnerProductSpaceRealComplex","instLTNat","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","map_pow","map_smul","one_mul","pow_zero","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"_private.GinibrePoincare.Analysis.GinibreEqualityConjugateProjection.0.GinibrePoincare.ginibreEquality_conjugate_mode_quotient_projection._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","ClosedSubmodule.toSubmodule","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","Subtype","UniformSpace.toTopologicalSpace","fact_one_le_two_ennreal","instHAdd","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.add","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.sub","AddSubgroup.zero","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddZeroClass","ClosedSubmodule.toSubmodule","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCompleteSpace","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreFiniteQuotientDegreeClosedSpan","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSub.hSub","InnerProductSpace.toNormedSpace","Int","Int.instNegInt","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.L2.innerProductSpace","MeasureTheory.Lp","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instCompleteSpace","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule.instHasOrthogonalProjectionOfCompleteSpace","Submodule.starProjection","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instCommCStarAlgebraComplex","instHAdd","instHSub","instLTNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"_private.GinibrePoincare.Analysis.GinibreEqualityConjugateProjection.0.GinibrePoincare.ginibreEquality_conjugate_mode_quotient_projection._proof_1_2","type_dependencies":["Eq","False","GinibrePoincare.vandermondeDegree","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","Subtype","Subtype.val","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","GinibrePoincare.vandermondeDegree","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","Subtype","Subtype.val","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","name":"_private.GinibrePoincare.Analysis.GinibreEqualityConjugateProjection.0.GinibrePoincare.ginibreLp_star_complex_smul","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.instStarRing","Complex.measurableSpace","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.ginibreMeasure","HSMul.hSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instStarSubtypeAEEqFunMemAddSubgroup","Membership.mem","Module.toDistribMulAction","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCStarAlgebra.toNonUnitalNormedRing","NonUnitalCStarAlgebra.toNormedSpace","NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Ring.toSemiring","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instCommCStarAlgebraComplex","instHSMul","instOfNatAtLeastTwo","instOfNatNat","starRingEnd"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CStarAlgebra.toCStarRing","CStarAlgebra.toNormedRing","CStarRing.to_normedStarGroup","CommCStarAlgebra.toCStarAlgebra","CommCStarAlgebra.toNonUnitalCommCStarAlgebra","CommCStarAlgebra.toNormedCommRing","CommMagma.toMul","CommSemiring.toSemiring","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.i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rePoincare.realToMixedVariables","_private.GinibrePoincare.Analysis.GinibreEqualityMixedPolynomial.0.GinibrePoincare.realToMixedVariables._proof_1","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat","ite"],"value_dependencies":["AddMonoidAlgebra.algebra","AddMonoidAlgebra.semiring","AlgHom","Algebra.id","CommSemiring.toSemiring","Complex","Complex.instCommSemiring","Eq.refl","Fin","Finsupp","Finsupp.instAddMonoid","GinibrePoincare.GinibreMixedPolynomial","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","Prod","_private.GinibrePoincare.Analysis.GinibreEqualityMixedPolynomial.0.GinibrePoincare.realToMixedVariables","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityPolynomial","name":"_private.GinibrePoincare.Analysis.GinibreEqualityPolynomial.0.GinibrePoincare.ginibreEquality_affine_homogeneous_part._proof_1_2","type_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","False","Fin","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","GinibrePoincare.ConfigurationPolynomial","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Ne","Not","OfNat.ofNat","instLENat","instOfNatNat"],"value_dependencies":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Complex","Complex.instCommSemiring","DFunLike.coe","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","GT.gt","GinibrePoincare.ConfigurationPolynomial","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","MulZeroClass.toZero","MvPolynomial.totalDegree","Nat","Nat.cast","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.lt_or_gt_of_ne","Ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityPolynomial","name":"_private.GinibrePoincare.Analysis.GinibreEqualityPolynomial.0.GinibrePoincare.ginibreEquality_affine_homogeneous_part._simp_1_1","type_dependencies":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0"],"value_dependencies":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.degree_eq_zero_iff","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityPolynomial","name":"_private.GinibrePoincare.Analysis.GinibreEqualityPolynomial.0.GinibrePoincare.ginibreEquality_homogeneous_one_expansion._simp_1_1","type_dependencies":["And","Eq","Finsupp","Finsupp.single","OfNat.ofNat","Or","Zero","Zero.toOfNat0"],"value_dependencies":["And","Eq","Finsupp","Finsupp.single","Finsupp.single_eq_single_iff","OfNat.ofNat","Or","Zero","Zero.toOfNat0","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreEqualityWeakAffine","name":"_private.GinibrePoincare.Analysis.GinibreEqualityWeakAffine.0.GinibrePoincare.ginibreEquality_full_weak_affine._proof_1_1","type_dependencies":["False","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instLENat","in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eroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.backwardEulerResolventMultiplier_graph_identity._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_1","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","two_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_2","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","three_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_3","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","four_ne_zero","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_4","type_dependencies":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dependencies":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_5","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","name":"_private.GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier.0.GinibrePoincare.resolventEulerMultiplier_eq_rate._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAd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orem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly.0.GinibrePoincare.ginibreHamiltonianOU_noise_coefficient._simp_1_5","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly.0.GinibrePoincare.ginibreHamiltonianOU_noise_coefficient._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly.0.GinibrePoincare.ginibreHamiltonianOU_noise_coefficient._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianOriginalEquilibriumReversal","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianOriginalEquilibriumReversal.0.GinibrePoincare.ginibreOriginalEquilibriumPathLaw_reverse._simp_1_1","type_dependencies":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dependencies":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness.0.GinibrePoincare.ginibreDrivenPath_finite_interval_unique._simp_1_1","type_dependencies":["AddGroup.toSubtractionMonoid","Eq","LE.le","NegZeroClass.toZero","Norm.norm","NormedAddGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","OfNat.ofNat","Real","Real.instLE","Real.instZero","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0"],"value_dependencies":["AddGroup.toSubtractionMonoid","Eq","LE.le","NegZeroClass.toZero","Norm.norm","NormedAddGroup","NormedAddGroup.toAddGroup","NormedAddGroup.toNorm","OfNat.ofNat","Real","Real.instLE","Real.instZero","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","norm_le_zero_iff","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness","name":"_private.GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness.0.GinibrePoincare.ginibreDrivenPath_finite_interval_unique._simp_1_2","type_dependencies":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub"],"value_dependencies":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub","propext","sub_eq_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"_private.GinibrePoincare.Analysis.GinibreIntegrationByParts.0.GinibrePoincare.coordinateDirection_eq_re_smul_real_add_im_smul_imagina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inormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.differentiable","ContDiff.exp","ContDiff.mul","ContDiff.neg","DenselyNormedField.toNontriviallyNormedField","Differentiable.differentiableAt","DifferentiableAt","Distrib.toMul","ENat","ENat.top_ne_zero._simp_1","Eq","Eq.mpr","Eq.trans","False","Field.toSemifield","Fin","Fin.fintype","GinibrePoincare.Configuration","GinibrePoincare.configurationNormSq","GinibrePoincare.contDiff_configurationNormSq","GinibrePoincare.gaussianWeight","HMul.hMul","HasDistribNeg.toInvolutiveNeg","InnerProductSpace.toNormedSpace","InvolutiveNeg.toNeg","Nat","Nat.cast","Neg.neg","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.toModule","Not","OfNat.ofNat","Pi.Function.module","Pi.addCommGroup","Pi.normedAddCommGroup","Pi.normedSpace","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.exp","Real.instAddCommGroup","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.coe_eq_zero._simp_1","WithTop.some","WithTop.zero","Zero.toOfNat0","congrArg","contDiff_const","funext","id","instDistribOfSemiring","instHMul","instInnerProductSpaceRealComplex","instTopENat","instZeroENat","neg_mul","not_false_eq_true","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreIntegrationByParts","name":"_private.GinibrePoincare.Analysis.GinibreIntegrationByParts.0.GinibrePoincare.differentiableAt_vandermondeWeight","type_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt","Field.toSemifield","Fin","GinibrePoincare.Configuration","GinibrePoincare.vandermondeWeight","InnerProductSpace.toNormedSpace","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommGroup","Pi.topologicalSpace","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.differentiable_im","Complex.differentiable_re","Complex.im","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSemiring","Complex.normSq","Complex.normSq_apply","Complex.re","ContDiff.differentiable","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Differentiable.differentiableAt","Diffe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sis.GinibreTransitionAnalyticLocalRegularityDensityQuotient","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient.0.GinibrePoincare.ginibreLocalRegularity_weighted_resolvent_cutoff_gradient._simp_1_4","type_dependencies":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dependencies":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient.0.GinibrePoincare.ginibreLocalRegularity_weighted_resolvent_cutoff_gradient._simp_1_5","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient.0.GinibrePoincare.ginibreLocalRegularity_weighted_resolvent_cutoff_gradient._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient.0.GinibrePoincare.ginibreLocalRegularity_weighted_resolvent_cutoff_gradient._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalization","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalization.0.GinibrePoincare.ginibreLocalRegularity_localize_elliptic_equation._simp_1_1","type_dependencies":["Distrib.toMul","Eq","Finset","Finset.sum","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"],"value_dependencies":["Distrib.toMul","Eq.symm","Finset","Finset.mul_sum","Finset.sum","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalizedData","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalizedData.0.GinibrePoincare.compact_sum","type_dependencies":["BorelSpace","Complex","Complex.instAddCommMonoid","Complex.instZero","FiniteDimensional","Finset.sum","Finset.univ","Fintype","HasCompactSupport","InnerProductSpace","InnerProductSpace.toNormedSpace","MeasurableSpace","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instDivisionRing","Real.instRCLike","Real.normedField","SeminormedAddCommGroup.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZeroClass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atCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.neg","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubgroupClass.toNegMemClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddZeroClass","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","Distrib.toAdd","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq.refl","Eq.symm","Eq.trans","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_constg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.AEEqFun.instAddMonoid","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","Nat","Neg.neg","NegMemClass.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedRing.toRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instRing","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.semiring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.addCommGroup","Submodule.addCommMonoid","Submodule.addSubgroupClass","Submodule.addSubmonoidClass","Submodule.module","Submodule.setLike","Submodule.zero","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","UniformSpace.toTopologicalSpace","Zero.toOfNat0","fact_one_le_two_ennreal","instDistribOfSemiring","instHAdd","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLTNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instTopologicalSpaceSubtype","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison","name":"_private.GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison.0.GinibrePoincare.ginibreSymmetricContractionSemigroup_eq_from_actual_laplace._abel_1_2","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroup.toAddGroup","AddSubgroupClass.sub","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","CommRing.toNonUnitalCommRing","Complex","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibreFullValueL2","GinibrePoincare.GinibreFullValueL2._proof_1","GinibrePoincare.ginibreFullSymmetricResolvent","GinibrePoincare.ginibreFullSymmetricValues","GinibrePoincare.ginibreMeasure","HSub.hSub","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalRing.toIsSemitopologicalRing","LT.lt","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp.instAddCommGroup","MeasureTheory.Lp.instModule","MeasureTheory.Lp.instNormedAddCommGroup","Membership.mem","NNReal","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNon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","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_2","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","three_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_3","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","four_ne_zero","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_4","type_dependencies":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dependencies":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_5","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeGradient","name":"_private.GinibrePoincare.Analysis.MagnitudeGradient.0.GinibrePoincare.realGradientNormSq_magnitude._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeNullSets","name":"_private.GinibrePoincare.Analysis.MagnitudeNullSets.0.GinibrePoincare.blockMagnitudes_pos_ae._simp_1_1","type_dependencies":["Eq","Not"],"value_dependencies":["Classical.not_not","Not","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeNullSets","name":"_private.GinibrePoincare.Analysis.MagnitudeNullSets.0.GinibrePoincare.ginibre_coordinates_ne_zero_ae._simp_1_1","type_dependencies":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dependencies":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MagnitudeNullSets","name":"_private.GinibrePoincare.Analysis.MagnitudeNullSets.0.GinibrePoincare.ginibre_coordinates_ne_zero_ae._simp_1_2","type_dependencies":["Eq","Not"],"value_dependencies":["Classical.not_not","Not","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.MatrixCayleyChart","name":"_private.GinibrePoincare.Analysis.MatrixCayleyChart.0.GinibrePoincare.matrixCayley_inverseCayley._a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NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toPseudoMetricSpace","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","contDiff_const","fderiv","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHAdd","instInnerProductSpaceRealComplex","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarBochner.0.GinibrePoincare.planarDbar_adjoint_coercivity._simp_1_1","type_dependencies":["Eq","Function.support","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","Zero","Zero.toOfNat0"],"value_dependencies":["Function.mem_support","Function.support","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","Zero","Zero.toOfNat0","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarBochner.0.GinibrePoincare.planarDerivative_comm","type_dependencies":["Complex","Complex.instNormedAddCommGroup","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","GinibrePoincare.planarDerivative","InnerProductSpace.toNormedSpace","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NormedAddCommGroup.toSeminormedAddCommGroup","OfNat.ofNat","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","WithTop","WithTop.natCast","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","ContDiff.contDiffAt","ContDiffAt.isSymmSndFDerivAt","ContinuousLinearMap","ContinuousLinearMap.addCommGroup","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.funLike","ContinuousLinearMap.module","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.trans","Field.toSemifield","GinibrePoincare.planarDerivative","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsSymmSndFDerivAt.eq","IsTopologicalRing.toIsSemitopologicalRing","LE.le","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","Std.le_refl._simp_1","True","UniformSpace.toTopologicalSpace","WithTop","WithTop.instPreorder","WithTop.natCast","_private.GinibrePoincare.Analysis.NonQuadraticDbarBochner.0.GinibrePoincare.planarDerivative_second","congrArg","congrFun'","fderiv","id","instInnerProductSpaceRealComplex","instIsRCLikeNormedField","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat","instPreorderENat","instReflLe","minSmoothness","minSmoothness_of_isRCLikeNormedField","of_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"_private.GinibrePoi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SeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instZero","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAddCommGroup","Real.instCommSemiring","Real.instRCLike","Real.instRing","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","RingHom.id","RingHomCompTriple.ids","RingHomIsometric.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.add","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","congrArg","congrFun","congrFun'","differentiableAt_const","eq_self","fderiv","fderiv_clm_apply","fderiv_fun_const","id","instAddENat","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCharZeroENat","instCommSemiringENat","instCompleteLinearOrderENat","instHAdd","instInnerProductSpaceRealComplex","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instLinearOrderENat","instMulZeroClassOfSemiring","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","instZeroENat","of_eq_true","smulCommClass_self","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarBochner","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarBochner.0.GinibrePoincare.planar_component_derivative","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","Eq","Field.toSemifield","GinibrePoincare.planarDerivative","InnerProductSpace.toNormedSpace","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","fderiv","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Differentiable","DifferentiableAt.hasFDerivAt","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","EMetricSpace.metrizableSpace","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","Function.comp","GinibrePoincare.planarDerivative","HasFDerivAt.comp","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsModuleTopology.toContinuousSMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toIsModuleTopology","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instRCLike","Real.metricSpace","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomCompTriple.ids","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","TopologicalSpace.t2Space_of_metrizableSpace","UniformSpace.toTopologicalSpace","congrArg","fderiv","id","instInnerProductSpaceRealComplex","instIsTopologicalRingReal","instPolynormableSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planarComplexifiedTest_adjoint","type_dependencies":["Complex","Complex.I","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSub","Complex.ofReal","ContDiff","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarComplexifiedTest","GinibrePoincare.planarDbarAdjoint","GinibrePoincare.planarDerivative","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.semiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.commRing","Complex.instAdd","Complex.instAddCommMonoid","Complex.instCharZero","Complex.instCommSemiring","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","ContinuousLinearMap.zero_apply","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarComplexifiedTest","GinibrePoincare.planarDbarAdjoint","GinibrePoincare.planarDbarOfParts._proof_1","GinibrePoincare.planarDerivative","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isRat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroClass.zero_mul","NNRat.rawCast","NPow.toPow","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Rat.rawCast","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planarComplexifiedTest_fderiv","add_zero","congr","congrArg","congrFun'","fderiv","fderiv_const_apply","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","rfl","sub_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planarComplexifiedTest_fderiv","type_dependencies":["AddCommGroup.toAddCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instMul","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","ENat.instNatCast","Eq","Field.toSemifield","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarComplexifiedTest","GinibrePoincare.planarDerivative","HMul.hMul","HasCompactSupport","InnerProductSpace.toNormedSpace","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fderiv","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddMonoidWithOne.toNatCast","Algebra.to_smulCommClass","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.instAddCommMonoid","Complex.instField","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instT2Space","Complex.ofReal","Complex.ofRealCLM","ContDiff","ContDiff.differentiable","ContinuousLinearMap","ContinuousLinearMap.comp","ContinuousLinearMap.funLike","ContinuousLinearMap.hasFDerivAt","ContinuousLinearMap.instIsSMulApply","ContinuousLinearMap.instSMul","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DifferentiableAt.hasFDerivAt","Distrib.toMul","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Field.toSemifield","Function.comp","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarComplexifiedTest","GinibrePoincare.planarDerivative","HMul.hMul","HSMul.hSMul","HasCompactSupport","HasFDerivAt","HasFDerivAt.comp","HasFDerivAt.const_mul","HasFDerivAt.fderiv","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedRing.toNonUnitalSeminormedRing","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toIsTopologicalRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toAlgebra","NormedAlgebra.toNormedSpace","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedRing.toNonUnitalNormedRing","NormedRing.toRing","NormedRing.toSeminormedRing","NormedSpace.complexToReal","NormedSpace.toModule","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","PolynormableSpace.continuousSMul","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toAddCommGroup","Ring.toNonAssocRing","Ring.toSemiring","RingHom.id","RingHomCompTriple.ids","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.natCast","WithTop.zero","Zero.toOfNat0","congrArg","congrFun'","fderiv","id","instAddMonoidWithOneENat","instCharZeroENat","instDistribOfSemiring","instHMul","instHSMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","instPolynormableSpace","instSMulOfMul","instZeroENat","smul_apply"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planar_gauge_pairing_ae","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","Complex.re","ContDiff","ContDiff.of_le","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq.refl","Field.toDivisionRing","Filter.EventuallyEq","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbarAdjoint","GinibrePoincare.planarPotentialGaugeTest","GinibrePoincare.planarUngaugedL2Function","GinibrePoincare.planarWeightedAdjointTestL2","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","Membership.mem","Nat","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHMul","instInnerProductSpaceRealComplex","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddUnits","Bool","Bool.true","CanonicallyOrderedCommMonoid.toUniqueAddUnits","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CommSemiring.toSemiring","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteLattice","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","Complex.ofReal","Complex.re","ContDiff","ContDiff.of_le","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENat","ENat.instNatCast","Eq","Eq.mpr","Eq.refl","Field.toDivisionRing","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.PlanarCompactTest","GinibrePoincare.PlanarLebesgueL2","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbarAdjoint","GinibrePoincare.planarPotentialGaugeTest","GinibrePoincare.planarUngaugedL2Function","GinibrePoincare.planarWeightedAdjointTestL2","GinibrePoincare.planarWeightedAdjointTestMap","GinibrePoincare.planarWeightedAdjointTestMap_gauge","GinibrePoincare.planarWeightedAdjointTestMap_memLp","HDiv.hDiv","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearMap","LinearMap.instFunLike","LinearOrder.toDecidableEq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Lp.instModule","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","Membership.mem","Nat","Nat.cast","Nat.cast_one","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instRCLike","Real.instZero","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.semiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Submodule","Submodule.addCommMonoid","Submodule.module","Submodule.setLike","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","Unique.instSubsingleton","WithTop","WithTop.addMonoidWithOne","WithTop.instIsOrderedRing","WithTop.instPartialOrder","WithTop.instSemiring","WithTop.natCast","WithTop.one","Zero.toOfNat0","_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planar_transfer_real_scalar","congrArg","id","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instHDiv","instHMul","instInnerProductSpaceRealComplex","instLinearOrderENat","instNoZeroDivisorsENat","instNontrivialENat","instOfNatAtLeastTwo","instOfNatNat","instOneENat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarGauge","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarGauge.0.GinibrePoincare.planar_transfer_real_scalar","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.ofReal","Complex.re","Eq","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InvolutiveStar.toStar","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Real","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.im","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","DFunLike.coe","Distrib.toAdd","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Inner.inner","InnerProductSpace.toInner","Int","Int.negOfNat","Int.ofNat","Int.rawCast","InvolutiveStar.toStar","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.cast_zero","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Real","Real.commRing","Real.instAdd","Real.instCommSemiring","Real.instMul","Real.instNeg","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","RingHom","RingHom.instFunLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toMonoid","Semiring.toNonAssocSemiring","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congr","congrArg","congrFun'","id","inferInstance","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","rfl","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_adjoint_compact","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedField","Complex.instZero","DFunLike.coe","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarAdjointTestMap","GinibrePoincare.planarCompactTestSpace","HasCompactSupport","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule.addCommMonoid","Submodule.module","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","And.right","CommSemiring.toSemiring","Complex","Complex.I","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSemiring","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Field.toSemifield","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbarOfParts._proof_1","GinibrePoincare.planarDerivative","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","HasCompactSupport.add","HasCompactSupport.fderiv_apply","HasCompactSupport.mul_left","HasCompactSupport.sub","InnerProductSpace.toNormedSpace","Membership.mem","MulZeroClass.toMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.instMul","Pi.instSub","PseudoMetricSpace.toUniformSpace","Real","Real.denselyNormedField","Real.instRCLike","Real.normedField","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule","Submodule.setLike","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","fderiv","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_adjoint_continuous","type_dependencies":["Complex","Complex.instAddCommMonoid","Complex.instNormedAddCommGroup","Complex.instNormedField","ContDiff","Continuous","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","ENat","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarAdjointTestMap","GinibrePoincare.planarCompactTestSpace","InnerProductSpace.toNormedSpace","LinearMap","LinearMap.instFunLike","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedField","Real.semiring","RingHom.id","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","Submodule.addCommMonoid","Submodule.module","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","instInnerProductSpaceRealComplex","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","And.left","Bool","Bool.false","CommSemiring.toSemiring","Complex","Complex.I","Complex.addGroupWithOne","Complex.continuous_ofReal","Complex.instAdd","Complex.instAddCommMonoid","Complex.instDivInvMonoid","Complex.instField","Complex.instMul","Complex.instNatCast","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instOne","Complex.instSub","Complex.instZero","Complex.ofReal","ContDiff","ContDiff.continuous","ContDiff.continuous_fderiv","Continuous","Continuous.add","Continuous.clm_apply","Continuous.comp","Continuous.mul","Continuous.sub","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.topologicalSpace","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DivInvMonoid.toDiv","ENat","ENat.instNatCast","Eq.refl","Field.toDivisionRing","Field.toSemifield","Function.comp","GinibrePoincare.PlanarCompactTest","GinibrePoincare.planarCompactTestSpace","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarDbarOfParts._proof_1","GinibrePoincare.planarDerivative","HDiv.hDiv","HMul.hMul","HSub.hSub","HasCompactSupport","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.to_continuousSub","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Membership.mem","Nat.cast_one","Nat.cast_zero","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.Function.module","Pi.addCommMonoid","Pi.instMul","Pi.instSub","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toNonAssocSemiring","SetLike.instMembership","Submodule","Submodule.setLike","Subtype.property","Subtype.val","UniformSpace.toTopologicalSpace","WithTop","WithTop.addMonoidWithOne","WithTop.charZero","WithTop.natCast","WithTop.one","WithTop.zero","Zero.toOfNat0","continuous_const","fderiv","instAddMonoidWithOneENat","instCharZeroENat","instHDiv","instHMul","instHSub","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOneENat","instZeroENat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_half_weight_continuous","type_dependencies":["Complex","Complex.instNormedField","Continuous","GinibrePoincare.planarPotentialHalfWeight","Nat","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace"],"value_dependencies":["CommRing.toNonUnitalCommRing","Complex","Complex.continuous_ofReal","Complex.instNormedField","Complex.ofReal","Continuous","Continuous.comp","Continuous.div_const","Continuous.mul","DivInvMonoid.toDiv","GinibrePoincare.planarCompactTestSpace._proof_2","GinibrePoincare.planarPotentialHalfWeight","HDiv.hDiv","HMul.hMul","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalRing.toIsSemitopologicalRing","IsTopologicalRing.toIsTopologicalSemiring","IsTopologicalSemiring.toContinuousMul","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","Pi.instMul","PseudoMetricSpace.toUniformSpace","Real","Real.commRing","Real.continuous_exp","Real.exp","Real.instDivInvMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_const","id","instHDiv","instHMul","instIsTopologicalRingReal","instOfNatAtLeastTwo","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarL2","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_half_weight_inner","type_dependencies":["AddCommMonoid.toAddMonoid","Complex","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.re","Eq","GinibrePoincare.planarPotentialHalfWeight","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InvolutiveStar.toStar","Nat","Nat.cast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Real","Real.exp","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","SeminormedCommRing.toNonUnitalSeminormedCommRing","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","instHMul","instInnerProductSpaceRealComplex"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","CommRing.toRing","CommSemiring.toSemiring","Complex","Complex.im","Complex.instCommSemiring","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedField","Complex.instStarRing","Complex.mul_im","Complex.mul_re","Complex.ofReal","Complex.re","DFunLike.coe","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.inst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inormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","UniformSpace.toTopologicalSpace","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instSetLike","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instStarRing","Complex.measurableSpace","Complex.re","ContinuousENorm.toENorm","DenselyNormedField.toNormedField","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Eq.mpr","Filter.mp_mem","Filter.univ_mem'","GinibrePoincare.planarPotentialHalfWeight","HMul.hMul","Inner.inner","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","InvolutiveStar.toStar","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.cast","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.inner_def","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp","MeasureTheory.Lp._proof_4","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.MemLp","MeasureTheory.MemLp.coeFn_toLp","MeasureTheory.MemLp.toLp","MeasureTheory.ae","MeasureTheory.integral","MeasureTheory.integral_congr_ae","Membership.mem","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.exp","Real.instMul","Real.instNatCast","Real.instNeg","Real.instRCLike","Real.normedAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Set","Set.instMembership","Set.ofPred","SetLike.instMembership","Star.star","StarAddMonoid.toInvolutiveStar","StarRing.toStarAddMonoid","Subtype","Subtype.val","UniformSpace.toTopologicalSpace","_private.GinibrePoincare.Analysis.NonQuadraticDbarL2.0.GinibrePoincare.planar_half_weight_inner","congrArg","id","instHMul","instInnerProductSpaceRealComplex","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticDbarMollification","name":"_private.GinibrePoincare.Analysis.NonQuadraticDbarMollification.0.GinibrePoincare.planar_component_locallyIntegrable","type_dependencies":["Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","DFunLike.coe","InnerProductSpace.toNormedSpace","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","Real","Real.instAddCommMonoid","Real.instRCLike","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["And","And.casesOn","And.intro","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.measurableSpace","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.integrable_comp","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Exists.casesOn","Exists.intro","Filter","Filter.instMembership","InnerProductSpace.toNormedSpace","MeasureTheory.IntegrableAtFilter","MeasureTheory.IntegrableOn","MeasureTheory.LocallyIntegrable","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","Membership.mem","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instRCLike","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomIsometric.ids","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toModule","Semiring.toNonAssocSemiring","Set","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace","nhds"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticEntropyBochner","name":"_private.GinibrePoincare.Analysis.NonQuadraticEntropyBochner.0.GinibrePoincare.compact_deriv_integral_zero","type_dependencies":["CommSemiring.toSemiring","ContDiff","DenselyNormedField.toNontriviallyNormedField","ENat","Eq","Field.toSemifield","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.integral","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toSeminormedAddCommGroup","NormedField.toField","OfNat.ofNat","One.toOfNat1","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instAddCommGroup","Real.instRCLike","Real.instZero","Real.measureSpace","Real.normedAddCommGroup","Real.pseudoMetricSpace","Semifield.toCommSemiring","Semiring.toModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.one","Zero.toOfNat0","deriv","instOneENat"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Bool","Bool.false","BorelSpace.opensMeasurable","CommRing.toRing","CommSemiring.toSemiring","ContDiff","ContDiff.continuous","ContDiff.deriv'","ContDiff.differentiable","Continuous","Continuous.integrable_of_hasCompactSupport","ContinuousLinearMap","ContinuousLinearMap.funLike","ContinuousLinearMap.instIsZeroApply","ContinuousLinearMap.zero","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivisionRing.toRing","ENat","ENormedAddCommMonoid.toESeminormedAddCommMonoid","ESeminormedAddCommMonoid.toESeminormedAddMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","FiniteDimensional.rclike_to_real","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","HasCompactSupport","HasCompactSupport.deriv","Iff.mpr","InnerProductSpace.toNormedSpace","Int","Int.negOfNat","Int.ofNat","Int.rawCast","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_eq_false","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.lt_of_eq_of_lt","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_ze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","Complex.borelSpace","Complex.continuous_normSq","Complex.instNormedField","Complex.instProperSpace","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Continuous","Continuous.aestronglyMeasurable","Continuous.comp","DFunLike.coe","EMetricSpace.toPseudoEMetricSpace","Fin","Function.comp","GinibrePoincare.Configuration","LE.le","MeasurableSpace.pi","MeasureTheory.Integrable.mono'","MeasureTheory.IsProbabilityMeasure","MeasureTheory.IsZeroOrProbabilityMeasure.toIsFiniteMeasure","MeasureTheory.Measure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae_of_all","MeasureTheory.instIsZeroOrProbabilityMeasureOfIsProbabilityMeasure","MeasureTheory.integrable_const","MetricSpace.toEMetricSpace","MonoidWithZeroHom","MonoidWithZeroHom.funLike","Nat","Norm.norm","NormedAddCommGroup.toNorm","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","Pi.opensMeasurableSpace","Pi.topologicalSpace","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","Real","Real.instLE","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.pseudoMetricSpace","Real.semiring","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","continuous_apply","continuous_pi","instCountableFin","instMulZeroOneClassOfSemiring","instSecondCountableTopologyReal","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticKostlan","name":"_private.GinibrePoincare.Analysis.NonQuadraticKostlan.0.GinibrePoincare.factor_mass_valid","type_dependencies":["And","CommSemiring.toCommMonoid","ENNReal","ENNReal.instCommSemiring","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","Fin","Fin.fintype","Finset.prod","Finset.univ","LT.lt","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Top.top","Zero.toOfNat0"],"value_dependencies":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","And.intro","CommMonoid.toMonoid","CommMonoidWithZero.toCommMonoid","CommMonoidWithZero.toMonoidWithZero","CommSemiring.toCommMonoid","CommSemiring.toCommMonoidWithZero","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instCanonicallyOrderedAdd","ENNReal.instCommSemiring","ENNReal.instNoZeroDivisors","ENNReal.instNontrivial","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.lt_top_of_mul_ne_top_left","Eq","Eq.rec","Eq.symm","Fin","Fin.fintype","Finset","Finset.erase","Finset.instSetLike","Finset.mem_univ","Finset.mul_prod_erase","Finset.prod","Finset.prod_ne_zero_iff","Finset.univ","HMul.hMul","Iff.mp","Iff.mpr","LT.lt","LT.lt.ne","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Ne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","Top.top","Zero.toOfNat0","instDecidableEqFin","instDistribOfSemiring","instHMul","instIsBotZeroClass","ne_of_gt","pos_iff_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticKostlan","name":"_private.GinibrePoincare.Analysis.NonQuadraticKostlan.0.GinibrePoincare.integrable_kostlanWeight'","type_dependencies":["Complex","Complex.measurableSpace","Fin","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.kostlanWeight","MeasurableSpace.pi","MeasureTheory.Integrable","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","PseudoMetricSpace.toUniformSpace","Real","Real.normedCommRing","Real.pseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","UniformSpace.toTopologicalSpace"],"value_dependencies":["Complex","Complex.instNorm","Complex.instSemiring","Complex.measurableSpace","Complex.normSq","Complex.sq_norm","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Eq.symm","Fin","Fin.fintype","Fin.val","Finset","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finset.univ","GinibrePoincare.Configuration","GinibrePoincare.complexGaussianMeasure","GinibrePoincare.integrable_prod_norm_pow_complexGaussianMeasure","GinibrePoincare.kostlanWeight","HMul.hMul","HPow.hPow","MeasurableSpace.pi","MeasureTheory.Integrable","Membership.mem","Monoid.toNPow","MonoidWithZeroHom","MonoidWithZeroHom.funLike","NPow.toPow","Nat","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedCommRing.toSeminormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instCommMonoid","Real.instMonoid","Real.normedCommRing","Real.pseudoMetricSpace","Real.semiring","SeminormedAddCommGroup.toSeminormedAddGroup","Seminorme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italNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Pi.Function.module","Pi.addCommMonoid","Prod","Prod.instMeasurableSpace","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toInnerProductSpaceReal","Real","Real.denselyNormedField","Real.instRCLike","Real.normedAddCommGroup","Ring.toSemiring","RingHom.id","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","Semiring.toModule","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","Submodule.addCommMonoid","Submodule.module","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","TensorProduct","TensorProduct.addCommMonoid","TensorProduct.instModule","UniformSpace.toTopologicalSpace","WithTop","WithTop.natCast","Zero.toOfNat0","fact_one_le_two_ennreal","instHAdd","instHSub","instInnerProductSpaceRealComplex","instOfNat","instOfNatAtLeastTwo","instOfNatNat","measureSpaceOfInnerProductSpace","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProductPlaneL2Mollification","name":"_private.GinibrePoincare.Analysis.NonQuadraticProductPlaneL2Mollification.0.GinibrePoincare.instVAddInvariantMeasureProdComplexVolume_ginibrePoincare._proof_1","type_dependencies":["Complex","Complex.borelSpace","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","FiniteDimensional.rclike_to_real","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.VAddInvariantMeasure","Prod","Prod.instAdd","instInnerProductSpaceRealComplex","instVAddOfAdd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","ContinuousAdd.measurableAdd","Field.toDivisionRing","FiniteDimensional.rclike_to_real","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableVAdd.toMeasurableConstVAdd","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddLeftInvariant.vaddInvariantMeasure","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsAddLeftInvariant","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Prod","Prod.borelSpace","Prod.instAdd","Prod.instMeasurableSpace","Prod.separatelyContinuousAdd","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instSeparatelyContinuousAddOfContinuousAdd","instTopologicalSpaceProd","instVAddOfAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableVAdd_of_add","measureSpaceOfInnerProductSpace","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticProjectionTensorization","name":"_private.GinibrePoincare.Analysis.NonQuadraticProjectionTensorization.0.GinibrePoincare.orthogonalProjection_composition_error._abel_1_1","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommS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cide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticRadialConfinement","name":"_private.GinibrePoincare.Analysis.NonQuadraticRadialConfinement.0.GinibrePoincare.radial_laplacian_quadratic_lower_bound._simp_1_1","type_dependencies":["Eq","LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Ioi","Set.instMembership"],"value_dependencies":["LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Ioi","Set.instMembership","Set.mem_Ioi","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticRadiusLaw","name":"_private.GinibrePoincare.Analysis.NonQuadraticRadiusLaw.0.GinibrePoincare.potentialPolynomialVolume_squaredRadius._proof_1_1","type_dependencies":["Eq","False","HAdd.hAdd","HMul.hMul","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instDecidableEq","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_mul","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.isZero","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.mul_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.mul","Lean.Omega.LinearCombo.mul_eval","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.decidableBAll","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","id","instAddNat","instDecidableEqBool","instDecidableOr","instHAdd","instHMul","instHSub","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticRadiusLaw","name":"_private.GinibrePoincare.Analysis.NonQuadraticRadiusLaw.0.GinibrePoincare.potentialPolynomialVolume_squaredRadius._proof_1_2","type_dependencies":["Eq","False","HAdd.hAdd","HMul.hMul","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instDecidableEq","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_mul","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.isZero","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.mul_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.mul","Lean.Omega.LinearCombo.mul_eval","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.decidableBAll","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","id","instAddNat","instDecidableEqBool","instDecidableOr","instHAdd","instHMul","instHSub","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticSeparatedConvolution","name":"_private.GinibrePoincare.Analysis.NonQuadraticSeparatedConvolution.0.GinibrePoincare.instVAddInvariantMeasureProdComplexVolume_ginibrePoincare_1._proof_1","type_dependencies":["Complex","Complex.borelSpace","Complex.instAdd","Complex.instNormedAddCommGroup","Complex.instRCLike","Complex.measurableSpace","FiniteDimensional.rclike_to_real","MeasureTheory.Measure.prod.measureSpace","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.VAddInvariantMeasure","Prod","Prod.instAdd","instInnerProductSpaceRealComplex","instVAddOfAdd","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddGroupWithOne.toAddGroup","Complex","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAdd","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instRCLike","Complex.measurableSpace","ContinuousAdd.measurableAdd","Field.toDivisionRing","FiniteDimensional.rclike_to_real","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasurableVAdd.toMeasurableConstVAdd","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddLeftInvariant.vaddInvariantMeasure","MeasureTheory.Measure.prod","MeasureTheory.Measure.prod.instIsAddLeftInvariant","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.instSFiniteOfSigmaFinite","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","Prod","Prod.borelSpace","Prod.instAdd","Prod.instMeasurableSpace","Prod.separatelyContinuousAdd","PseudoMetricSpace.toUniformSpace","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instSeparatelyContinuousAddOfContinuousAdd","instTopologicalSpaceProd","instVAddOfAdd","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measurableVAdd_of_add","measureSpaceOfInnerProductSpace","secondCountableTopologyEither_of_right","secondCountable_of_proper"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification.0.GinibrePoincare.complexBump_compact","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.normed","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","HasCompactSupport","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddGroup","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instZero","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_zero","ContDiffBump","ContDiffBump.hasCompactSupport_normed","ContDiffBump.normed","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","HasCompactSupport.comp_left","InnerProductSpace.toNormedSpace","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.MeasureSpace.volume","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.instZero","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeightedProductMollification.0.GinibrePoincare.complexBump_continuous","type_dependencies":["Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.normed","Continuous","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["Complex","Complex.borelSpace","Complex.continuous_ofReal","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instZero","Complex.measurableSpace","Complex.ofReal","ContDiffBump","ContDiffBump.continuous_normed","ContDiffBump.normed","Continuous.comp","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","InnerProductSpace.toNormedSpace","MeasureTheory.MeasureSpace.volume","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","Real","Real.instRCLike","Real.pseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","UniformSpace.toTopologicalSpace","Zero.toOfNat0","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeightedTranslations","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeightedTranslations.0.GinibrePoincare.planarWeightedTranslateL2_continuousOn_compact._abel_1_1","type_dependencies":["Complex","Complex.instAdd","Complex.instSub","Eq","HAdd.hAdd","HSub.hSub","instHAdd","instHSub"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.instNeg","Complex.instSub","Complex.instZero","Distrib.toAdd","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Int.instRing","Int.negOfNat","Int.ofNat","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Abel.const_add_termg","Mathlib.Tactic.Abel.subst_into_addg","Mathlib.Tactic.Abel.subst_into_negg","Mathlib.Tactic.Abel.term_add_termg","Mathlib.Tactic.Abel.term_atomg","Mathlib.Tactic.Abel.term_neg","Mathlib.Tactic.Abel.termg","Mathlib.Tactic.Abel.unfold_sub","Mathlib.Tactic.Abel.zero_termg","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","add_zero","instDistribOfSemiring","instHAdd","instHSub","instOfNat","neg_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeyl","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeyl.0.GinibrePoincare.planarRadialSmoothingBase_integral_pos._simp_1_2","type_dependencies":["Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Real.smoothTransition","Zero.toOfNat0"],"value_dependencies":["Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Real.smoothTransition","Real.smoothTransition.zero_iff_nonpos","Zero.toOfNat0","propext"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeyl","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeyl.0.GinibrePoincare.planar_real_kernel_convolution_assoc","type_dependencies":["AddCommMonoid.toAddMonoid","Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instSub","Complex.measurableSpace","Continuous","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toMulAction","Eq","HasCompactSupport","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","MeasureTheory.LocallyIntegrable","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","Module.toDistribMulAction","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedField.toNormedCommRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instMonoid","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","UniformSpace.toTopologicalSpace","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","Algebra.to_smulCommClass","And","And.casesOn","And.intro","BorelSpace.opensMeasurable","CommMonoid.toMonoid","CommRing.toCommMonoid","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instAddCommMonoid","Complex.instCommSemiring","Complex.instCompleteSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instMul","Complex.instNonUnitalCommRing","Complex.instNorm","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.measurableSpace","Complex.ofReal","Complex.ofReal_mul","Continuous","Continuous.aestronglyMeasurable","Continuous.locallyIntegrable","Continuous.norm","ContinuousAdd.measurableMul\u2082","ContinuousLinearMap","ContinuousLinearMap.addCommMonoid","ContinuousLinearMap.funLike","ContinuousLinearMap.lsmul","ContinuousLinearMap.module","ContinuousLinearMap.mul","ContinuousLinearMap.topologicalSpace","ContinuousNeg.measurableNeg","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toAdd","Distrib.toMul","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Filter","Filter.Eventually.of_forall","Filter.instMembership","HAdd.hAdd","HMul.hMul","HPow.hPow","HasCompactSupport","HasCompactSupport.comp_left","HasCompactSupport.continuous_convolution_left","HasCompactSupport.convolutionExists_left","InnerProductSpace.toNormedSpace","IsBoundedSMul.toUniformContinuousConstSMul","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","MeasureTheory.ConvolutionExists","MeasureTheory.ConvolutionExistsAt","MeasureTheory.Integrable.norm","MeasureTheory.IntegrableAtFilter","MeasureTheory.IntegrableOn","MeasureTheory.IsAddLeftInvariant.isAddRightInvariant","MeasureTheory.LocallyIntegrable","MeasureTheory.LocallyIntegrable.aestronglyMeasurable","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instInnerRegularOfPseudoMetrizableSpaceOfSigmaCompactSpaceOfBorelSpaceOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.Measure.restrict","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.convolution_assoc","MeasureTheory.instSFiniteOfSigmaFinite","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","Membership.mem","MetricSpace.toEMetricSpace","Module.toDistribMulAction","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instCompleteSpace","Real.instMonoid","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.metricSpace","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace","Set","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TopologicalSpace.SecondCountableTopology.to_separableSpace","UniformContinuousConstSMul.instContinuousConstSMul","UniformSpace.toTopologicalSpace","Zero.toOfNat0","congrArg","congrFun'","id","instDistribOfSemiring","instHAdd","instHMul","instHPow","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instMulZeroClassOfSemiring","instSecondCountableTopologyReal","instWeaklyLocallyCompactSpaceOfLocallyCompactSpace","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","nhds","norm_zero","rfl","secondCountableTopologyEither_of_right","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable","smulCommClass_self"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NonQuadraticWeyl","name":"_private.GinibrePoincare.Analysis.NonQuadraticWeyl.0.GinibrePoincare.planar_real_kernel_convolution_comm","type_dependencies":["Algebra.id","CommSemiring.toSemiring","Complex","Complex.borelSpace","Complex.instFiniteDimensionalReal","Complex.instNormedAddCommGroup","Complex.instSub","Complex.measurableSpace","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","Eq","InnerProductSpace.toNormedSpace","IsScalarTower.right","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.convolution","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","instInnerProductSpaceRealComplex","measureSpaceOfInnerProductSpace"],"value_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Algebra.id","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Complex","Complex.addCommGroup","Complex.addGroupWithOne","Complex.borelSpace","Complex.instField","Complex.instFiniteDimensionalReal","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instProperSpace","Complex.instSub","Complex.measurableSpace","ContinuousAdd.measurableAdd","ContinuousLinearMap.lsmul","ContinuousNeg.measurableNeg","DenselyNormedField.toNontriviallyNormedField","DistribMulAction.toDistribSMul","DistribMulAction.toMulAction","DistribSMul.toSMulZeroClass","EMetricSpace.toPseudoEMetricSpace","Eq","Eq.mpr","Field.toDivisionRing","Field.toSemifield","Filter.Eventually.of_forall","HSMul.hSMul","HSub.hSub","InnerProductSpace.toNormedSpace","IsScalarTower.left","IsScalarTower.right","IsSemitopologicalRing.toContinuousNeg","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular","MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite","MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instInnerRegularOfPseudoMetrizableSpaceOfSigmaCompactSpaceOfBorelSpaceOfSigmaFinite","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.MeasureSpace.toMeasurableSpace","MeasureTheory.MeasureSpace.volume","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.convolution_lsmul","MeasureTheory.convolution_lsmul_swap","MeasureTheory.integral","MeasureTheory.integral_congr_ae","MetricSpace.toEMetricSpace","Module.toDistribMulAction","NegZeroClass.toNeg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.id","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toMetricSpace","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","PseudoEMetricSpace.pseudoMetrizableSpace","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instCommSemiring","Real.instRCLike","Real.isBoundedSMul","Real.normedAddCommGroup","Real.normedCommRing","Ring.toSemiring","SMulZeroClass.toSMul","Semifield.toCommSemiring","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","SeminormedRing.toRing","Semiring.toModule","Semiring.toMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","congrArg","funext","id","instHSMul","instHSub","instInnerProductSpaceRealComplex","instIsAddHaarMeasureVolume","instSeparatelyContinuousAddOfContinuousAdd","locallyCompact_of_proper","measureSpaceOfInnerProductSpace","mul_comm","secondCountable_of_proper","sigmaCompactSpace_of_locallyCompact_secondCountable"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.NormalizedComplexHermite","name":"_private.GinibrePoincare.Analysis.NormalizedComplexHermite.0.GinibrePoincare.ComplexHermite.oneDimNormalization_succ","type_dependencies":["Eq","GinibrePoincare.ComplexHermite.oneDimNormalization","HAdd.hAdd","HMul.hMul","LT.lt","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instMul","Real.instNatCast","Real.instOne","Real.sqrt","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dependencies":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toRing","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GinibrePoincare.ComplexHermite.oneDimNormalization","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Int.rawCast","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","IsOrderedAddMonoid.toAddLeftMono","IsOrderedAddMonoid.toAddRightMono","IsOrderedRing.toMulPosMono","IsStrictOrderedRing.toIsOrderedRing","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrderedCommMonoidWithZero.toPosMulStrictMono","List.nil","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isIn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","instHSMul","instInnerProductSpaceRealComplex","instLENat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","mul_add","mul_left_comm","not_and._simp_1","of_eq_true","starRingEnd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorSpectrum","name":"_private.GinibrePoincare.Analysis.PolynomialGeneratorSpectrum.0.GinibrePoincare.ginibreFullGenerator_natural_spectrum_containment._proof_1","type_dependencies":["False","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HSub.hSub","Int","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorSpectrum","name":"_private.GinibrePoincare.Analysis.PolynomialGeneratorSpectrum.0.GinibrePoincare.ginibreFullGenerator_natural_spectrum_containment._simp_1_1","type_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.instSemiring","Complex.ofReal","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HSMul.hSMul","Module","Module.complexToReal","Module.toDistribMulAction","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instHSMul"],"value_dependencies":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.coe_smul","Complex.instSemiring","Complex.ofReal","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq.symm","HSMul.hSMul","Module","Module.complexToReal","Module.toDistribMulAction","Real","Real.instMonoid","Real.semiring","SMulZeroClass.toSMul","Semiring.toMonoid","SubNegMonoid.toAddMonoid","instHSMul"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorSymmetry","name":"_private.GinibrePoincare.Analysis.PolynomialGeneratorSymmetry.0.GinibrePoincare.polynomialGeneratorGraph_symmetry","type_dependencies":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instSemiring","Complex.measurableSpace","ENNReal","ENNReal.instAddCommMonoidWithOne","Eq","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.ginibreMeasure","GinibrePoincare.polynomialGeneratorGraph","Inner.inner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LE.le","MeasurableSpace.pi","MeasureTheory.AEEqFun","MeasureTheory.AEEqFun.instAddCommMonoid","MeasureTheory.AEEqFun.instAddGroup","MeasureTheory.L2.instInnerSubtypeAEEqFunMemAddSubgroupLpOfNatENNReal","MeasureTheory.Lp.instModule","Membership.mem","Nat","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedRing.toRing","NormedSpace.toIsBoundedSMul","OfNat.ofNat","Prod","Prod.fst","Prod.instAddCommMonoid","Prod.instModule","Prod.snd","Pseu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","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedSpace","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.normedAddCommGroup","Pi.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.im","RCLike.mul_im","RCLike.mul_re","RCLike.re","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddGroup","Real.instAddMonoid","Real.instMul","Real.instOne","Real.instRCLike","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.semiring","Ring.toSemiring","RingHom.id","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedAddCommGroup.toSeminormedAddGroup","SeminormedAddGroup.toContinuousENorm","SeminormedAddGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Top.top","UniformSpace.toTopologicalSpace","WithTop.some","Zero.toOfNat0","add_zero","congr","congrArg","congrFun'","funext","id","instDistribOfSemiring","instHAdd","instHMul","instHSub","instInnerProductSpaceRealComplex","instLTNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTopENat","integral_im","integral_re","mul_comm","mul_one","one_mul","sub_self","sub_zero","zero_add"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialGeneratorWeakCore","name":"_private.GinibrePoincare.Analysis.PolynomialGeneratorWeakCore.0.GinibrePoincare.polynomialEigenfunction_full_core_weak_equation._proof_1","type_dependencies":["False","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HSub.hSub","Int","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.PolynomialSectorGenerator","name":"_private.GinibrePoincare.Analysis.PolynomialSectorGenerator.0.GinibrePoincare.polynomialSectorBasisPair_mem_ambient_graph","type_dependencies":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSubgroup","AddSubgroup.instAddSubgroupClass","AddSubgroup.instSetLike","AddSubgroupClass.toAddSubmonoidClass","AddSubmonoidClass.toAddCommMonoid","AddSubmonoidClass.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Complex","Complex.addGroupWithOne","Complex.instAddCommMonoid","Complex.instField","Complex.instNeg","Complex.instNonUnitalCommRing","Complex.instNormedAddCommGroup","Complex.instNormedField","Complex.instRCLike","Complex.instRing","Complex.instSemiring","Complex.measurableSpace","Complex.ofReal","DFunLike.coe","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","ENNReal","ENNReal.instAddCommMonoidWithOne","Field.toDivisionRing","Fin","GinibrePoincare.Configuration","GinibrePoincare.GinibrePolynomialL2","GinibrePoincare.GinibrePolynomialL2._proof_1","GinibrePoincare.PolynomialEigenf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"module":"GinibrePoincare.Analysis.StrongConvexBoundedLipschitzLSIExtension","name":"_private.GinibrePoincare.Analysis.StrongConvexBoundedLipschitzLSIExtension.0.GinibrePoincare.norm_mollification_le","type_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","CommSemiring.toSemiring","ContDiffBump","ContDiffBump.normed","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","FiniteDimensional","InnerProductSpace.toNormedSpace","IsScalarTower.right","LE.le","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.convolution","NegZeroClass.toZero","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedSpace","NormedSpace.toModule","OfNat.ofNat","PseudoMetricSpace.toUniformSpace","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instCommSemiring","Real.instDivisionRing","Real.instLE","Real.instRCLike","Real.isBoundedSMul","Real.norm","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Ring.toSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toRing","Semiring.toModule","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","UniformSpace.toTopologicalSpace","Zero.toOfNat0"],"value_dependencies":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","Algebra.id","BorelSpace","BorelSpace.opensMeasurable","CommSemiring.toSemiring","ContDiff.continuous","ContDiffBump","ContDiffBump.contDiff_normed","ContDiffBump.hasCompactSupport_normed","ContDiffBump.integral_normed","ContDiffBump.nonneg_normed","ContDiffBump.normed","Continuous.integrable_of_hasCompactSupport","ContinuousLinearMap.lsmul","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","ENat","Eq","Eq.mpr","Eq.refl","ExistsContDiffBumpBase.instHasContDiffBumpOfFiniteDimensionalReal","Field.toSemifield","Filter.Eventually.of_forall","FiniteDimensional","FiniteDimensional.proper_real","HMul.hMul","HSMul.hSMul","HSub.hSub","HasSolidNorm.orderClosedTopology","InnerProductSpace.toNormedSpace","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsScalarTower.right","IsStrictOrderedModule.toIsOrderedModule","IsStrictOrderedRing.toIsStrictOrderedModule","LE.le","MeasurableSpace","MeasureTheory.Integrable","MeasureTheory.Integrable.mul_const","MeasureTheory.Measure","MeasureTheory.Measure.IsAddHaarMeasure","MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts","MeasureTheory.Measure.IsAddHaarMeasure.toIsOpenPosMeasure","MeasureTheory.Measure.instFunLike","MeasureTheory.Measure.instOuterMeasureClass","MeasureTheory.ae","MeasureTheory.convolution","MeasureTheory.integral","MeasureTheory.integral_mono_of_nonneg","MeasureTheory.integral_mul_const","MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts","MeasureTheory.norm_integral_le_integral_norm","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toSMulWithZero","MulZeroOneClass.toMulOneClass","NegZeroClass.toZero","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","Norm.norm","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toNorm","NormedAddCommGroup.toSeminormedAddCommGroup","NormedAlgebra.toNormedSpace","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toNormedRing","NormedCommRing.toSeminormedCommRing","NormedField.toField","NormedField.toNormedCommRing","NormedRing.toRing","NormedSpace","NormedSpace.toModule","NormedSpace.toNormSMulClass","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Pi.instZero","Preorder.toLE","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toNormedAlgebra","Real","Real.denselyNormedField","Real.instAddCommMonoid","Real.instAddGroup","Real.instCommSemiring","Real.instDivisionRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instOne","Real.instPreorder","Real.instRCLike","Real.instZero","Real.isBoundedSMul","Real.lattice","Real.norm","Real.norm_eq_abs","Real.normedAddCommGroup","Real.normedCommRing","Real.normedField","Real.partialOrder","Real.pseudoMetricSpace","Real.semiring","Ring.toSemiring","Semifield.toCommSemiring","SeminormedAddCommGroup.toPseudoMetricSpace","Seminorm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Poincare.Analysis.StrongConvexRadialLipschitzTransfer","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer.0.GinibrePoincare.realGradientNormSq_magnitude_at._simp_1_3","type_dependencies":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dependencies":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","four_ne_zero","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer.0.GinibrePoincare.realGradientNormSq_magnitude_at._simp_1_4","type_dependencies":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dependencies":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer.0.GinibrePoincare.realGradientNormSq_magnitude_at._simp_1_5","type_dependencies":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dependencies":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer.0.GinibrePoincare.realGradientNormSq_magnitude_at._simp_1_6","type_dependencies":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dependencies":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialLipschitzTransfer.0.GinibrePoincare.realGradientNormSq_magnitude_at._simp_1_7","type_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dependencies":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.StrongConvexRadialSymmetrizedLaw","name":"_private.GinibrePoincare.Analysis.StrongConvexRadialSymmetrizedLaw.0.GinibrePoincare.potential_magnitude_map_eq_symmetrizedRadiusProduct._simp_1_1","type_dependencies":["Eq","False","Fintype","Fintype.card","Nat","Nonempty","OfNat.ofNat","instOfNatNat"],"value_dependencies":["Eq","Fintype","Fintype.card","Fintype.card_ne_zero","Nat","Nonempty","OfNat.ofNat","eq_false","instOfNatNat"]},{"kind":"theorem","module":"GinibrePoincare.Analysis.SumRadiusGenerator","name":"_private.GinibrePoincare.Analysis.SumRadiusGenerator.0.GinibrePoincare.complexGinibrePregenerator_sumRadiusPolynomial._proof_1_2","type_dependencies":["Eq","False","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dependencies":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HSub.hSub","Int","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean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uousEvalConst","name":"ContinuousEvalConst.continuous_eval_const"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital","name":"ContinuousFunctionalCalculus"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital","name":"ContinuousFunctionalCalculus.compactSpace_spectrum"},{"module":"Mathlib.Topology.Algebra.GroupWithZero","name":"ContinuousInv\u2080.continuousAt_inv\u2080"},{"module":"Mathlib.MeasureTheory.Constructions.BorelSpace.Basic","name":"ContinuousInv\u2080.measurableInv"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.apply_symm_apply"},{"module":"Mathlib.Analysis.Calculus.FDeriv.Equiv","name":"ContinuousLinearEquiv.comp_right_fderiv"},{"module":"Mathlib.Analysis.Calculus.ContDiff.Basic","name":"ContinuousLinearEquiv.contDiff"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.continuous"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.continuousSemilinearEquivClass"},{"module":"Mathlib.Analysis.Calculus.FDeriv.Equiv","name":"ContinuousLinearEquiv.differentiable"},{"module":"Mathlib.Analysis.Calculus.FDeriv.Equiv","name":"ContinuousLinearEquiv.differentiableAt"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.equivLike"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.equivOfInverse"},{"module":"Mathlib.Analysis.Calculus.FDeriv.Equiv","name":"ContinuousLinearEquiv.fderiv"},{"module":"Mathlib.Analysis.Calculus.FDeriv.Equiv","name":"ContinuousLinearEquiv.hasFDerivAt"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.injective"},{"module":"Mathlib.MeasureTheory.Group.Measure","name":"ContinuousLinearEquiv.isAddHaarMeasure_map"},{"module":"Mathlib.Analysis.Normed.Operator.NNNorm","name":"ContinuousLinearEquiv.lipschitzWith"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.map_smul"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.mk"},{"module":"Mathlib.Analysis.Normed.Operator.Banach","name":"ContinuousLinearEquiv.ofBijective"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_1"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_2"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_3"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_4"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_5"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrLeft._proof_6"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrRight"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrRight._proof_1"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.piCongrRight._proof_2"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.prodComm"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.prodComm_apply"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.prodCongr"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.refl"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.symm"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.symm_apply_apply"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.toContinuousLinearMap"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.toHomeomorph"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.toLinearEquiv"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.trans"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.trans.congr_simp"},{"module":"Mathlib.Topology.Algebra.Module.Equiv","name":"ContinuousLinearEquiv.trans_toLinearEquiv"},{"module":"Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic","name":"ContinuousLinearMap"},{"module":"Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Invertible","name":"ContinuousLinearMap.IsInvertible"},{"module":"Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Invertible","name":"ContinuousLinearMap.IsInvertible.of_inverse"},{"module":"Mathlib.Analysis.InnerProductSpace.Positive","name":"ContinuousLinearMap.IsPositive"},{"module":"Mathlib.Analysis.InnerProductSpace.Positive","name":"ContinuousLinearMap.IsPositive.re_inner_nonneg_right"},{"module":"Mathlib.Topology.Alge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:"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.lt_of_eq_of_lt"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.lt_of_lt_of_eq"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.mul_eq"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.mul_neg"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.mul_nonpos"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.mul_zero_eq"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.natCast_nonneg"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.sub_neg_of_lt"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.sub_nonpos_of_le"},{"module":"Mathlib.Tactic.Linarith.Preprocessing","name":"Mathlib.Tactic.Linarith.without_one_mul"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.zero_lt_one"},{"module":"Mathlib.Tactic.Linarith.Lemmas","name":"Mathlib.Tactic.Linarith.zero_mul_eq"},{"module":"Mathlib.Tactic.LinearCombination.Lemmas","name":"Mathlib.Tactic.LinearCombination.add_eq_eq"},{"module":"Mathlib.Tactic.LinearCombination.Lemmas","name":"Mathlib.Tactic.LinearCombination.eq_of_eq"},{"module":"Mathlib.Tactic.LinearCombination.Lemmas","name":"Mathlib.Tactic.LinearCombination.eq_rearrange"},{"module":"Mathlib.Tactic.LinearCombination.Lemmas","name":"Mathlib.Tactic.LinearCombination.mul_const_eq"},{"module":"Mathlib.Tactic.LinearCombination.Lemmas","name":"Mathlib.Tactic.LinearCombination.mul_eq_const"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.add_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.add_eq_eval\u2081"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.atom_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.cons"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.eq_cons_cons"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.eq_cons_const"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.eval_algebraMap"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.neg_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.smul_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.sub_eq_eval"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.sub_eq_eval\u2081"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.sub_eq_eval\u2082"},{"module":"Mathlib.Tactic.Module","name":"Mathlib.Tactic.Module.NF.zero_sub_eq_eval"},{"module":"Mathlib.Tactic.NoncommRing","name":"Mathlib.Tactic.NoncommRing.nat_lit_mul_eq_nsmul"},{"module":"Mathlib.Tactic.Push","name":"Mathlib.Tactic.Push.not_and_eq"},{"module":"Mathlib.Tactic.Push","name":"Mathlib.Tactic.Push.not_exists._simp_1"},{"module":"Mathlib.Tactic.Push","name":"Mathlib.Tactic.Push.not_forall_eq"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_congr"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_mul"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_overlap_pf"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_overlap_pf_zero"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_add_gt"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_add_lt"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_add_overlap"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_add_zero"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.add_pf_zero_add"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.atom_pf"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.atom_pf'"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.coeff_one"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.const_pos"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.div_congr"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.div_pf"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.inv_congr"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.inv_mul"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.inv_single"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Tactic.Ring.Common.mul_add"},{"module":"Mathlib.Tactic.Ring.Common","name":"Mathlib.Ta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v.Defs","name":"MulEquiv.instMulEquivClass"},{"module":"Mathlib.Algebra.Prime.Lemmas","name":"MulEquiv.prime_iff"},{"module":"Mathlib.Algebra.Group.Hom.Defs","name":"MulHomClass"},{"module":"Mathlib.Algebra.Group.Monoid","name":"MulOne.toMul"},{"module":"Mathlib.Algebra.Group.Monoid","name":"MulOne.toOne"},{"module":"Mathlib.Algebra.Group.Monoid","name":"MulOneClass.toMulOne"},{"module":"Mathlib.Algebra.Opposites","name":"MulOpposite"},{"module":"Mathlib.Topology.Algebra.MulAction","name":"MulOpposite.continuousSMul"},{"module":"Mathlib.Algebra.Algebra.Opposite","name":"MulOpposite.instAlgebra"},{"module":"Mathlib.Algebra.Group.Opposite","name":"MulOpposite.instMonoid"},{"module":"Mathlib.Algebra.Opposites","name":"MulOpposite.instOne"},{"module":"Mathlib.Algebra.Ring.Opposite","name":"MulOpposite.instRing"},{"module":"Mathlib.Algebra.Ring.Opposite","name":"MulOpposite.instSemiring"},{"module":"Mathlib.Topology.Algebra.Constructions","name":"MulOpposite.instTopologicalSpaceMulOpposite"},{"module":"Mathlib.Algebra.Opposites","name":"MulOpposite.instZero"},{"module":"Mathlib.Algebra.Opposites","name":"MulOpposite.op"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Basic","name":"MulPosReflectLE.toMulPosReflectLT"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Defs","name":"MulPosStrictMono.toMulPosReflectLE"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroClass"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroClass.mul_zero"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroClass.toMul"},{"module":"Mathlib.Algebra.GroupWithZero.Action.Defs","name":"MulZeroClass.toOppositeSMulWithZero"},{"module":"Mathlib.Algebra.GroupWithZero.Action.Defs","name":"MulZeroClass.toSMulWithZero"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroClass.toZero"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroClass.zero_mul"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroOneClass.toMulOneClass"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"MulZeroOneClass.toMulZeroClass"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.instFunLikeForall"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.map_smul_univ"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.map_sum"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.mk"},{"module":"Mathlib.Analysis.Normed.Module.Multilinear.Basic","name":"MultilinearMap.mkContinuous"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.toFun"},{"module":"Mathlib.LinearAlgebra.Multilinear.Basic","name":"MultilinearMap.toLinearMap"},{"module":"Mathlib.Data.Multiset.Defs","name":"Multiset"},{"module":"Mathlib.Data.Multiset.Defs","name":"Multiset.Nodup"},{"module":"Mathlib.Data.Multiset.Fintype","name":"Multiset.ToType"},{"module":"Mathlib.Data.Multiset.Defs","name":"Multiset.card"},{"module":"Mathlib.Data.Multiset.Fintype","name":"Multiset.card_coe"},{"module":"Mathlib.Data.Multiset.Count","name":"Multiset.count"},{"module":"Mathlib.Data.Multiset.Filter","name":"Multiset.count_map"},{"module":"Mathlib.Data.Multiset.Filter","name":"Multiset.filter"},{"module":"Mathlib.Data.Multiset.Fintype","name":"Multiset.fintypeCoe"},{"module":"Mathlib.Data.Multiset.Defs","name":"Multiset.instMembership"},{"module":"Mathlib.Data.Multiset.MapFold","name":"Multiset.map"},{"module":"Mathlib.Data.Multiset.MapFold","name":"Multiset.map_map"},{"module":"Mathlib.Data.Multiset.Fintype","name":"Multiset.map_univ"},{"module":"Mathlib.Data.Finset.Dedup","name":"Multiset.mem_toFinset"},{"module":"Mathlib.Data.Multiset.MapFold","name":"Multiset.nodup_map_iff_inj_on"},{"module":"Mathlib.Algebra.BigOperators.Group.Multiset.Defs","name":"Multiset.prod"},{"module":"Mathlib.Data.Finset.Dedup","name":"Multiset.toFinset"},{"module":"Mathlib.Data.Finset.Card","name":"Multiset.toFinset_card_eq_card_iff_nodup"},{"module":"Mathlib.Data.Finset.Card","name":"Multiset.toFinset_card_le"},{"module":"Mathlib.Data.Finset.Card","name":"Multiset.toFinset_card_of_nodup"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_0"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_add"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_mul"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_mul_X_pow_eq_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_mul_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_ne_zero"},{"module":"Mathlib.Algebra.MvPolynomial.CommRing","name":"MvPolynomial.C_neg"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.C_pow"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.C_mul"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.coeff_eq_zero"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.mul"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.prod"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.sub"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.sum"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.IsHomogeneous.totalDegree"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.X"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.X_injective"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.X_mul_pderiv_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.X_pow_eq_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.aeval"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.aeval_C"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.aeval_X"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.aeval_X_left_apply"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.aeval_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.aeval_rename"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.algHom_C"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.algHom_ext"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.as_sum"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.coeff_C"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.coeff_C_mul"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.coeff_X"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.coeff_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.coeff_rename_mapDomain"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.coeff_sum"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.comp_aeval_apply"},{"module":"Mathlib.Topology.Algebra.MvPolynomial","name":"MvPolynomial.continuous_eval"},{"module":"Mathlib.Algebra.MvPolynomial.Derivation","name":"MvPolynomial.derivation_C"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_C"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_X"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.eval_eq_eval_mv_eval'"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_mul"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_ofNat"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_pow"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.eval_rename"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval_sum"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval\u2082Hom"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval\u2082Hom_X'"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.eval\u2082_C"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.ext"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.finSuccEquiv"},{"module":"Mathlib.Algebra.MvPolynomial.Funext","name":"MvPolynomial.funext"},{"module":"Mathlib.Algebra.MvPolynomial.Funext","name":"MvPolynomial.funext_set"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.homogeneousComponent"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.homogeneousComponent_C_mul"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.homogeneousComponent_isHomogeneous"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.induction_on"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.induction_on'"},{"module":"Mathlib.RingTheory.MvPolynomial.Basic","name":"MvPolynomial.instCharP"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.instIsCancelMulZeroOfIsCancelAdd"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.instIsDomainOfIsCancelAdd"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.instNoZeroDivisors"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.isHomogeneous_C"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.isHomogeneous_X"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.isHomogeneous_X_pow"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.le_totalDegree"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.map"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.map_C"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.map_X"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.map_injective"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.mem_support_iff"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.monomial_add_single"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.monomial_eq"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.monomial_mul"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.optionEquivLeft"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.optionEquivLeft_C"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.optionEquivLeft_X_none"},{"module":"Mathlib.Algebra.MvPolynomial.Equiv","name":"MvPolynomial.optionEquivLeft_X_some"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_C"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_C_mul"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_X"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_X_of_ne"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_X_self"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_mul"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_one"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_pow"},{"module":"Mathlib.Algebra.MvPolynomial.PDeriv","name":"MvPolynomial.pderiv_rename"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.prod_X_pow_eq_monomial"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.rename"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.renameEquiv"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.renameEquiv_apply"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.rename_C"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.rename_X"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.rename_homogeneousComponent"},{"module":"Mathlib.Algebra.MvPolynomial.Rename","name":"MvPolynomial.rename_rename"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.ringHom_ext"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.smul_eval"},{"module":"Mathlib.RingTheory.MvPolynomial.Homogeneous","name":"MvPolynomial.sum_homogeneousComponent"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.support"},{"module":"Mathlib.Algebra.MvPolynomial.Eval","name":"MvPolynomial.support_map_of_injective"},{"module":"Mathlib.Algebra.MvPolynomial.Basic","name":"MvPolynomial.support_sum_monomial_coeff"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_C"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_X_pow"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_eq_zero_iff_eq_C"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_finsetProd"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_finsetSum_le"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_mul"},{"module":"Mathlib.Algebra.MvPolynomial.NoZeroDivisors","name":"MvPolynomial.totalDegree_mul_of_isDomain"},{"module":"Mathlib.Algebra.MvPolynomial.Degrees","name":"MvPolynomial.totalDegree_zero"},{"module":"Mathlib.RingTheory.Polynomial.UniqueFactorization","name":"MvPolynomial.uniqueFactorizationMonoid"},{"module":"Mathlib.Topology.MetricSpace.Pseudo.Defs","name":"NNDist.nndist"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NNNorm.nnnorm"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NNNorm.toENorm"},{"module":"Mathlib.Data.Rat.Init","name":"NNRat"},{"module":"Mathlib.Topology.Instances.Rat","name":"NNRat.instContinuousSMulNNReal"},{"module":"Mathlib.Topology.Instances.Rat","name":"NNRat.instContinuousSMulOfIsScalarTowerOfRat"},{"module":"Mathlib.Topology.Instances.Rat","name":"NNRat.instContinuousSMulRatReal"},{"module":"Mathlib.Tactic.NormNum.Result","name":"NNRat.rawCast"},{"module":"Mathlib.Basic.NNReal.Defs","name":"NNReal"},{"module":"Mathlib.Basic.NNReal.Defs","name":"NNReal.abs_eq"},{"modul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sto_coe"},{"module":"Mathlib.Topology.Instances.NNReal.Lemmas","name":"NNReal.tendsto_coe_atTop"},{"module":"Mathlib.Basic.NNReal.Defs","name":"NNReal.toReal"},{"module":"Mathlib.Basic.NNReal.Basic","name":"NNReal.toReal_lt._simp_1"},{"module":"Mathlib.Basic.NNReal.Defs","name":"NNReal.zero_le_coe._simp_1"},{"module":"Mathlib.Algebra.Group.Monoid","name":"NPow.npow"},{"module":"Mathlib.Algebra.Group.Monoid","name":"NPow.toPow"},{"module":"Mathlib.Algebra.Group.Monoid","name":"NSMul.toSMul"},{"module":"Init.Prelude","name":"Nat"},{"module":"Mathlib.Data.Nat.Init","name":"Nat.AtLeastTwo"},{"module":"Init.Data.Nat.Basic","name":"Nat.add_assoc"},{"module":"Init.Data.Nat.Basic","name":"Nat.add_comm"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_eq_left._simp_1"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_eq_right._simp_1"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_eq_zero_iff._simp_1"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_left_cancel_iff._simp_1"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_lt_add_of_lt_of_le"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.add_one_mul_choose_eq"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_pos_left"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.add_right_cancel_iff._simp_1"},{"module":"Init.Data.Nat.Basic","name":"Nat.add_sub_cancel"},{"module":"Init.Data.Nat.Basic","name":"Nat.add_sub_cancel_left"},{"module":"Init.Data.Nat.Basic","name":"Nat.add_sub_of_le"},{"module":"Init.Core","name":"Nat.add_zero"},{"module":"Init.Prelude","name":"Nat.below"},{"module":"Init.Prelude","name":"Nat.ble"},{"module":"Init.Prelude","name":"Nat.brecOn"},{"module":"Init.Prelude","name":"Nat.brecOn.eq"},{"module":"Init.Prelude","name":"Nat.brecOn.go"},{"module":"Init.Data.Nat.Basic","name":"Nat.casesAuxOn"},{"module":"Init.Prelude","name":"Nat.casesOn"},{"module":"Init.Data.Cast","name":"Nat.cast"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_add"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_add._simp_1"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_add_one_ne_zero"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_eq_zero"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_eq_zero._simp_1"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_inj._simp_1"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_injective"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_ite"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_ite._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.cast_le"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.cast_le._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.cast_lt._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Basic","name":"Nat.cast_mul"},{"module":"Mathlib.Data.Nat.Cast.Basic","name":"Nat.cast_mul._simp_1"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"Nat.cast_ne_zero"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.cast_nonneg"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.cast_nonneg'"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.cast_nonneg._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_ofNat"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_one"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.cast_pos"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.cast_pos'"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.cast_pos._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Basic","name":"Nat.cast_pow"},{"module":"Mathlib.Data.Nat.Cast.Basic","name":"Nat.cast_pow._simp_1"},{"module":"Mathlib.Data.Int.Cast.Basic","name":"Nat.cast_pred"},{"module":"Mathlib.Algebra.Module.NatInt","name":"Nat.cast_smul_eq_nsmul"},{"module":"Mathlib.Data.Int.Cast.Basic","name":"Nat.cast_sub"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_succ"},{"module":"Mathlib.Algebra.BigOperators.Ring.Finset","name":"Nat.cast_sum"},{"module":"Mathlib.Algebra.BigOperators.Ring.Finset","name":"Nat.cast_sum._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Defs","name":"Nat.cast_zero"},{"module":"Mathlib.Algebra.Order.Floor.Defs","name":"Nat.ceil"},{"module":"Mathlib.Algebra.Order.Floor.Defs","name":"Nat.ceil_le"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.ceil_lt_add_one"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_eq_zero_of_lt"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_mul"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_mul_factorial_mul_factorial"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_mul_succ_eq"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_one_right"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_pos"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_self"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_succ_right_eq"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_succ_self_right"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_succ_succ"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_succ_succ'"},{"module":"Mathlib.Data.Nat.Choose.Basic","name":"Nat.choose_zero_right"},{"module":"Init.Prelude","name":"Nat.decLe"},{"module":"Init.Prelude","name":"Nat.decLt"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.decidableExistsFin"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.decidableExistsLT"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.decidableForallFin"},{"module":"Init.Data.Nat.Div.Basic","name":"Nat.div_eq_of_lt"},{"module":"Init.Data.Nat.Div.Basic","name":"Nat.div_lt_iff_lt_mul"},{"module":"Init.Data.Nat.Div.Basic","name":"Nat.div_mul_le_self"},{"module":"Mathlib.Logic.Encodable.Basic","name":"Nat.encodable"},{"module":"Init.Data.Nat.Basic","name":"Nat.eq_zero_of_le_zero"},{"module":"Init.Data.Nat.Basic","name":"Nat.eq_zero_of_not_pos"},{"module":"Init.Data.Nat.Basic","name":"Nat.exists_eq_succ_of_ne_zero"},{"module":"Mathlib.Data.Nat.Factorial.Basic","name":"Nat.factorial"},{"module":"Mathlib.Data.Nat.Factorial.Basic","name":"Nat.factorial_ne_zero"},{"module":"Mathlib.Data.Nat.Factorial.Basic","name":"Nat.factorial_pos"},{"module":"Mathlib.Data.Nat.Factorial.Basic","name":"Nat.factorial_succ"},{"module":"Mathlib.Data.Nat.Find","name":"Nat.find"},{"module":"Mathlib.Data.Nat.Find","name":"Nat.find_min'"},{"module":"Mathlib.Data.Nat.Find","name":"Nat.find_spec"},{"module":"Mathlib.Algebra.Order.Floor.Defs","name":"Nat.floor"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.floor_le"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.floor_le_of_le"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.floor_mono"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.floor_natCast"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instAddCancelCommMonoid"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instAddCommMonoid"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instAddCommSemigroup"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instAddMonoid"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instAddMonoidWithOne"},{"module":"Init.Data.Nat.Basic","name":"Nat.instAssociativeHMul"},{"module":"Mathlib.Data.Nat.Init","name":"Nat.instAtLeastTwoHAddOfNat"},{"module":"Mathlib.Algebra.Order.Group.Nat","name":"Nat.instCanonicallyOrderedAdd"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instCharZero"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instCommMonoid"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instCommSemiring"},{"module":"Init.Data.Nat.Basic","name":"Nat.instCommutativeHMul"},{"module":"Init.Prelude","name":"Nat.instDiv"},{"module":"Mathlib.Algebra.Order.Group.Nat","name":"Nat.instIsOrderedAddMonoid"},{"module":"Mathlib.Algebra.Order.Group.Nat","name":"Nat.instIsOrderedCancelAddMonoid"},{"module":"Mathlib.Algebra.Order.Ring.Nat","name":"Nat.instIsStrictOrderedRing"},{"module":"Mathlib.Order.Lattice.Nat","name":"Nat.instLattice"},{"module":"Mathlib.Data.Nat.Basic","name":"Nat.instLinearOrder"},{"module":"Mathlib.Algebra.Order.Ring.Nat","name":"Nat.instLinearOrderedCommMonoidWithZero"},{"module":"Mathlib.Order.Interval.Finset.Nat","name":"Nat.instLocallyFiniteOrder"},{"module":"Init.Data.Nat.Basic","name":"Nat.instMax"},{"module":"Mathlib.MeasureTheory.MeasurableSpace.Instances","name":"Nat.instMeasurableSpace"},{"module":"Mathlib.Topology.Instances.Nat","name":"Nat.instMetricSpace"},{"module":"Init.Prelude","name":"Nat.instMod"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instMonoid"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instMulOneClass"},{"module":"Mathlib.Algebra.GroupWithZero.Nat","name":"Nat.instMulZeroClass"},{"module":"Mathlib.Algebra.GroupWithZero.Nat","name":"Nat.instMulZeroOneClass"},{"module":"Init.Data.Nat.Basic","name":"Nat.instNeZeroSucc"},{"module":"Mathlib.Order.Nat","name":"Nat.instNoMaxOrder"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instNonUnitalNonAssocSemiring"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instNonUnitalSemiring"},{"module":"Mathlib.Data.Nat.Basic","name":"Nat.instNontrivial"},{"module":"Mathlib.Algebra.Group.Nat.Defs","name":"Nat.instOne"},{"module":"Mathlib.Order.Nat","name":"Nat.instOrderBot"},{"module":"Mathlib.Algebra.Order.Group.Nat","name":"Nat.instOrderedSub"},{"module":"Mathlib.Data.Nat.Basic","name":"Nat.instPartialOrder"},{"module":"Mathlib.Data.Nat.Basic","name":"Nat.instPreorder"},{"module":"Mathlib.Algebra.Ring.Nat","name":"Nat.instSemiring"},{"module":"Mathlib.Algebra.Order.Star.Basic","name":"Nat.instStarOrderedRing"},{"module":"Mathlib.Algebra.Star.Basic","name":"Nat.instStarRing"},{"module":"Mathlib.Data.Nat.SuccPred","name":"Nat.instSuccAddOrder"},{"module":"Mathlib.Algebra.Order.ZeroLEOne","name":"Nat.instZeroLEOneClass"},{"module":"Mathlib.Logic.Function.Iterate","name":"Nat.iterate"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_add_left"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_add_right"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.le_ceil"},{"module":"Mathlib.Algebra.Order.Floor.Defs","name":"Nat.le_floor_iff"},{"module":"Mathlib.Data.Nat.Init","name":"Nat.le_induction"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.le_mul_of_pos_left"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.le_mul_of_pos_right"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_of_lt"},{"module":"Init.Prelude","name":"Nat.le_of_lt_succ"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_of_not_gt"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_of_not_lt"},{"module":"Init.Data.Nat.Basic","name":"Nat.le_of_succ_le"},{"module":"Init.Prelude","name":"Nat.le_refl"},{"module":"Init.Prelude","name":"Nat.le_succ"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.left_eq_add._simp_1"},{"module":"Mathlib.Algebra.Order.Floor.Semiring","name":"Nat.lt_floor_add_one"},{"module":"Init.Prelude","name":"Nat.lt_of_lt_of_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.lt_of_not_ge"},{"module":"Init.Prelude","name":"Nat.lt_of_not_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.lt_of_succ_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.lt_or_gt_of_ne"},{"module":"Init.Data.Nat.Basic","name":"Nat.lt_succ_iff"},{"module":"Init.Prelude","name":"Nat.lt_succ_of_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.lt_succ_of_lt"},{"module":"Init.Prelude","name":"Nat.lt_succ_self"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.lt_two_pow_self"},{"module":"Init.Data.Nat.Div.Basic","name":"Nat.mod_add_div"},{"module":"Init.Data.Nat.Div.Basic","name":"Nat.mod_eq_of_lt"},{"module":"Init.Prelude","name":"Nat.mod_lt"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.mod_succ"},{"module":"Init.Prelude","name":"Nat.mul"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.mul_add_div"},{"module":"Init.Data.Nat.Basic","name":"Nat.mul_comm"},{"module":"Init.Data.Nat.Basic","name":"Nat.mul_le_mul_left"},{"module":"Init.Data.Nat.Basic","name":"Nat.mul_le_mul_right"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.mul_ne_zero"},{"module":"Init.Prelude","name":"Nat.mul_pos"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.mul_right_cancel"},{"module":"Init.Data.Nat.Basic","name":"Nat.ne_of_gt"},{"module":"Init.Data.Nat.Basic","name":"Nat.ne_of_lt"},{"module":"Init.Data.Nat.Basic","name":"Nat.not_le_of_lt"},{"module":"Init.Prelude","name":"Nat.not_lt_zero"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.ofNat_nonneg._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"Nat.ofNat_pos._simp_1"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.one_le_iff_ne_zero"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.one_le_ofNat._simp_1"},{"module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"Nat.one_lt_ofNat._simp_1"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.pair"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.pair_lt_pair_left"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.pair_lt_pair_right"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.pair_unpair"},{"module":"Init.Data.Nat.Basic","name":"Nat.pos_of_ne_zero"},{"module":"Init.Prelude","name":"Nat.pow"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.pow_eq_zero._simp_1"},{"module":"Mathlib.Tactic.NormNum.Result","name":"Nat.rawCast"},{"module":"Init.Prelude","name":"Nat.rec"},{"module":"Init.Data.Nat.Basic","name":"Nat.recAux"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.right_eq_add._simp_1"},{"module":"Mathlib.Data.Nat.Init","name":"Nat.strong_induction_on"},{"module":"Init.Data.Nat.Basic","name":"Nat.sub_add_cancel"},{"module":"Init.Prelude","name":"Nat.sub_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.sub_le_sub_right"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.sub_sub_self"},{"module":"Init.Prelude","name":"Nat.succ"},{"module":"Mathlib.Data.Nat.Basic","name":"Nat.succ_injective"},{"module":"Init.Data.Nat.Basic","name":"Nat.succ_le_of_lt"},{"module":"Init.Prelude","name":"Nat.succ_le_succ"},{"module":"Init.Data.Nat.Basic","name":"Nat.succ_le_succ_iff"},{"module":"Init.Data.Nat.Basic","name":"Nat.succ_mul"},{"module":"Init.Prelude","name":"Nat.succ_pos"},{"module":"Init.Data.Nat.Lemmas","name":"Nat.succ_sub_one"},{"module":"Mathlib.Algebra.Group.Nat.Units","name":"Nat.unique_addUnits"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.unpair"},{"module":"Mathlib.Data.Nat.Pairing","name":"Nat.unpair_pair"},{"module":"Init.Prelude","name":"Nat.zero"},{"module":"Init.Prelude","name":"Nat.zero_le"},{"module":"Init.Data.Nat.Basic","name":"Nat.zero_sub"},{"module":"Init.Data.Cast","name":"NatCast"},{"module":"Init.Data.Cast","name":"NatCast.natCast"},{"module":"Init.Core","name":"Ne"},{"module":"Mathlib.Order.BoundedOrder.Basic","name":"Ne.lt_top"},{"module":"Init.Core","name":"Ne.symm"},{"module":"Init.Data.NeZero","name":"NeZero"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"NeZero.charZero_one"},{"module":"Init.Data.NeZero","name":"NeZero.mk"},{"module":"Mathlib.Algebra.GroupWithZero.NeZero","name":"NeZero.one"},{"module":"Init.Prelude","name":"Neg"},{"module":"Init.Prelude","name":"Neg.neg"},{"module":"Mathlib.Algebra.Group.Subgroup.Defs","name":"NegMemClass.neg"},{"module":"Mathlib.Algebra.Group.DivInvMonoid","name":"NegZeroClass.toNeg"},{"module":"Mathlib.Algebra.Group.DivInvMonoid","name":"NegZeroClass.toZero"},{"module":"Mathlib.Order.Interval.Set.Infinite","name":"NoMinOrder.infinite"},{"module":"Mathlib.Algebra.GroupWithZero.Defs","name":"NoZeroDivisors"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocCommRing.toNonAssocRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocRing.toAddCommGroupWithOne"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocRing.toNonUnitalNonAssocRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocSemiring.toAddCommMonoidWithOne"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocSemiring.toMulZeroOneClass"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonAssocSemiring.toNonUnitalNonAssocSemiring"},{"module":"Mathlib.Analysis.Normed.Operator.Mul","name":"NonUnitalAlgHom.Lmul._proof_1"},{"module":"Mathlib.Analysis.Normed.Operator.Mul","name":"NonUnitalAlgHom.Lmul._proof_3"},{"module":"Mathlib.Algebra.Algebra.NonUnitalHom","name":"NonUnitalAlgHomClass.instLinearMapClass"},{"module":"Mathlib.Algebra.Algebra.NonUnitalHom","name":"NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass"},{"module":"Mathlib.Algebra.Algebra.NonUnitalHom","name":"NonUnitalAlgSemiHomClass.toMulHomClass"},{"module":"Mathlib.Analysis.CStarAlgebra.Classes","name":"NonUnitalCStarAlgebra.toIsScalarTower"},{"module":"Mathlib.Analysis.CStarAlgebra.Classes","name":"NonUnitalCStarAlgebra.toNonUnitalNormedRing"},{"module":"Mathlib.Analysis.CStarAlgebra.Classes","name":"NonUnitalCStarAlgebra.toNormedSpace"},{"module":"Mathlib.Analysis.CStarAlgebra.Classes","name":"NonUnitalCStarAlgebra.toSMulCommClass"},{"module":"Mathlib.Analysis.CStarAlgebra.Classes","name":"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommRing.toNonUnitalCommSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommRing.toNonUnitalNonAssocCommRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommRing.toNonUnitalRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommSemiring.toCommSemigroup"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalCommSemiring.toNonUnitalSemiring"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital","name":"NonUnitalContinuousFunctionalCalculus"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric","name":"NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocCommSemiring.toCommMagma"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocRing"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocRing.toAddCommGroup"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocRing.toHasDistribNeg"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocSemiring.toAddCommMonoid"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocSemiring.toDistrib"},{"module":"Mathlib.GroupTheory.GroupAction.Ring","name":"NonUnitalNonAssocSemiring.toDistribSMul"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalNonAssocSemiring.toMulZeroClass"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalNormedCommRing.toNonUnitalNormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalNormedRing.toNonUnitalRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalNormedRing.toNonUnitalSeminormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalNormedRing.toNormedAddCommGroup"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalRing.toNonUnitalNonAssocRing"},{"module":"Mathlib.Algebra.Ring.Hom.Defs","name":"NonUnitalRingHomClass.toMulHomClass"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalSeminormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Lemmas","name":"NonUnitalSeminormedRing.toIsTopologicalRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalSeminormedRing.toNonUnitalRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalSeminormedRing.toPseudoMetricSpace"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NonUnitalSeminormedRing.toSeminormedAddCommGroup"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalSemiring.toNonUnitalNonAssocSemiring"},{"module":"Mathlib.Algebra.Ring.Defs","name":"NonUnitalSemiring.toSemigroupWithZero"},{"module":"Init.Prelude","name":"Nonempty"},{"module":"Init.Prelude","name":"Nonempty.intro"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances","name":"Nonneg.instNonUnitalContinuousFunctionalCalculus"},{"module":"Mathlib.Algebra.Order.Nonneg.Basic","name":"Nonneg.zero"},{"module":"Mathlib.Algebra.Algebra.Spectrum.Quasispectrum","name":"NonnegSpectrumClass"},{"module":"Mathlib.Basic.Nontrivial.Defs","name":"Nontrivial"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NontriviallyNormedField"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NontriviallyNormedField.infinite"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NontriviallyNormedField.toNormedField"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"Norm"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"Norm.norm"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormMulClass.toNoZeroDivisors"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormOneClass.norm_one"},{"module":"Mathlib.Topology.Separation.Regular","name":"NormalSpace"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.mk"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.toAddCommGroup"},{"module":"Mathlib.Analysis.Normed.Group.Continuity","name":"NormedAddCommGroup.toENormedAddCommMonoid"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.toMetricSpace"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.toNorm"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.toNormedAddGroup"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddCommGroup.toSeminormedAddCommGroup"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddGroup"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddGroup.toAddGroup"},{"module":"Mathlib.Analysis.Normed.Group.Continuity","name":"NormedAddGroup.toENormedAddMonoid"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddGroup.toNorm"},{"module":"Mathlib.Analysis.Normed.Group.Defs","name":"NormedAddGroup.toSeminormedAddGroup"},{"module":"Mathlib.Analysis.Normed.Group.Uniform","name":"NormedAddGroup.to_isIsometricVAdd_right"},{"module":"Mathlib.Analysis.Normed.Group.AddTorsor","name":"NormedAddTorsor.toAddTorsor"},{"module":"Mathlib.Analysis.Complex.Basic","name":"NormedAlgebra.complexToReal"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedAlgebra.id"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedAlgebra.norm_smul_le"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedAlgebra.toAlgebra"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedAlgebra.toNormedSpace"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedCommRing.toCommRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedCommRing.toNonUnitalNormedCommRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedCommRing.toNormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedCommRing.toSeminormedCommRing"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedDivisionRing.toDivisionRing"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedDivisionRing.toNorm"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedDivisionRing.toNormMulClass"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedDivisionRing.toNormedRing"},{"module":"Mathlib.Analysis.Normed.Field.Lemmas","name":"NormedDivisionRing.to_isTopologicalDivisionRing"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedDivisionRing.to_normOneClass"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedField.toField"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedField.toMetricSpace"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedField.toNorm"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedField.toNormedCommRing"},{"module":"Mathlib.Analysis.Normed.Field.Basic","name":"NormedField.toNormedDivisionRing"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedField.toNormedSpace"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Units","name":"NormedRing.inverse_continuousAt"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing.toMetricSpace"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing.toNonUnitalNormedRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing.toNorm"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing.toRing"},{"module":"Mathlib.Analysis.Normed.Ring.Basic","name":"NormedRing.toSeminormedRing"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace"},{"module":"Mathlib.Analysis.Complex.Basic","name":"NormedSpace.complexToReal"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp.congr_simp"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.expSeries_div_hasSum_exp"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp_analytic"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp_continuous"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp_mem_unitary_of_mem_skewAdjoint"},{"module":"Mathlib.Analysis.Normed.Algebra.Exponential","name":"NormedSpace.exp_zero"},{"module":"Mathlib.Analysis.Normed.Module.Convex","name":"NormedSpace.instPathConnectedSpace"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace.mk"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace.restrictScalars"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace.toIsBoundedSMul"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace.toModule"},{"module":"Mathlib.Analysis.Normed.Module.Basic","name":"NormedSpace.toNormSMulClass"},{"module":"Mathlib.Analysis.CStarAlgebra.Basic","name":"NormedStarGroup"},{"module":"Mathlib.Analysis.CStarAlgebra.Basic","name":"NormedStarGroup.to_continuousStar"},{"module":"Init.Prelude","name":"Not"},{"module":"Init.Core","name":"Not.intro"},{"module":"Mathlib.Analysis.ODE.ExistUnique","name":"ODE_solution_unique"},{"module":"Mathlib.Analysis.ODE.ExistUnique","name":"ODE_solution_unique_of_eventually"},{"module":"Init.Prelude","name":"OfNat"},{"module":"Init.Prelude","name":"OfNat.ofNat"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"OfNat.ofNat_ne_one._simp_1"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"OfNat.ofNat_ne_zero"},{"module":"Mathlib.Algebra.CharZero.Defs","name":"OfNat.ofNat_ne_zero._simp_1"},{"module":"Init.Prelude","name":"One"},{"module":"Init.Data.Zero","name":"One.toOfNat1"},{"module":"Mathlib.Algebra.Group.Hom.Defs","name":"OneHom"},{"module":"Mathlib.Algebra.Group.Hom.Defs","name":"OneHom.mk"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Continuity","name":"OpenPartialHomeomorph.continuousAt_symm"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.injOn"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.left_inv"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.map_source"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.open_source"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.open_target"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.right_inv"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.symm"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.toFun'"},{"module":"Mathlib.Topology.OpenPartialHomeomorph.Defs","name":"OpenPartialHomeomorph.toPartialHomeomorph"},{"module":"Mathlib.MeasureTheory.Constructions.BorelSpace.Basic","name":"OpensMeasurableSpace"},{"module":"Init.Prelude","name":"Option"},{"module":"Init.Prelude","name":"Option.casesOn"},{"module":"Mathlib.Data.Option.Basic","name":"Option.casesOn'"},{"module":"Init.Prelude","name":"Option.ctorIdx"},{"module":"Mathlib.Basic.Countable.Basic","name":"Option.instCountable"},{"module":"Init.Prelude","name":"Option.none"},{"module":"Init.Prelude","name":"Option.some"},{"module":"Init.Core","name":"Option.some.injEq"},{"module":"Init.Prelude","name":"Or"},{"module":"Init.Prelude","name":"Or.casesOn"},{"module":"Init.Prelude","name":"Or.elim"},{"module":"Init.Prelude","name":"Or.inl"},{"module":"Init.Prelude","name":"Or.inr"},{"module":"Init.Prelude","name":"Or.resolve_left"},{"module":"Init.Prelude","name":"Or.resolve_right"},{"module":"Mathlib.Order.CompleteBooleanAlgebra","name":"Order.Frame.toHeytingAlgebra"},{"module":"Mathlib.Algebra.Order.SuccPred","name":"Order.add_one_le_iff._simp_1"},{"module":"Mathlib.Algebra.Order.SuccPred","name":"Order.lt_add_one_iff._simp_1"},{"module":"Mathlib.Algebra.Order.SuccPred","name":"Order.lt_one_iff._simp_1"},{"module":"Mathlib.Order.Bounds.Basic","name":"OrderBot.bddBelow"},{"module":"Mathlib.Order.BoundedOrder.Basic","name":"OrderBot.toBot"},{"module":"Mathlib.Order.OrderDual","name":"OrderDual"},{"module":"Mathlib.Data.Fint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Polynomial.Eval.Defs","name":"Polynomial.eval_one"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval_pow"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval_prod"},{"module":"Mathlib.Algebra.Polynomial.Eval.SMul","name":"Polynomial.eval_smul"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval_sub"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval_zero"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_C"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_X"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_add"},{"module":"Mathlib.Algebra.Polynomial.Eval.Coeff","name":"Polynomial.eval\u2082_hom"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_monomial"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_mul"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_neg"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.eval\u2082_sub"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.ext"},{"module":"Mathlib.Algebra.Polynomial.Roots","name":"Polynomial.finite_setOfPred_isRoot"},{"module":"Mathlib.Algebra.Polynomial.Coeff","name":"Polynomial.finsetSum_coeff"},{"module":"Mathlib.Analysis.Calculus.Deriv.Polynomial","name":"Polynomial.hasDerivAt"},{"module":"Mathlib.Algebra.Polynomial.Eval.Coeff","name":"Polynomial.hom_eval\u2082"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.induction_on'"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instAdd"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instMul"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instNatCast"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instNeg"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instOne"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instSub"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.instZero"},{"module":"Mathlib.Algebra.Polynomial.Degree.Defs","name":"Polynomial.leadingCoeff"},{"module":"Mathlib.Algebra.Polynomial.Degree.Defs","name":"Polynomial.leadingCoeff_ne_zero"},{"module":"Mathlib.Algebra.Polynomial.Eval.Defs","name":"Polynomial.map"},{"module":"Mathlib.Algebra.Polynomial.Roots","name":"Polynomial.mem_roots"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.module"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.monomial"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.monomial_mul_monomial"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.monomial_zero_right"},{"module":"Mathlib.Algebra.Polynomial.Coeff","name":"Polynomial.mul_coeff_zero"},{"module":"Mathlib.Algebra.Polynomial.Degree.Defs","name":"Polynomial.natDegree"},{"module":"Mathlib.Algebra.Polynomial.Derivative","name":"Polynomial.natDegree_derivative"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.nodup_roots"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.nodup_roots_iff_of_splits"},{"module":"Mathlib.Algebra.Polynomial.RingDivision","name":"Polynomial.prime_X_sub_C"},{"module":"Mathlib.RingTheory.Polynomial.Resultant.Basic","name":"Polynomial.resultant"},{"module":"Mathlib.RingTheory.Polynomial.Resultant.Basic","name":"Polynomial.resultant_eq_zero_iff"},{"module":"Mathlib.RingTheory.Polynomial.Resultant.Basic","name":"Polynomial.resultant_map_map"},{"module":"Mathlib.RingTheory.Polynomial.Resultant.Basic","name":"Polynomial.resultant_ne_zero"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.ring"},{"module":"Mathlib.Algebra.Polynomial.Roots","name":"Polynomial.roots"},{"module":"Mathlib.Algebra.Polynomial.Roots","name":"Polynomial.roots_multiset_prod_X_sub_C"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.semiring"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.separable_X_sub_C"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.separable_one"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.separable_one._simp_1"},{"module":"Mathlib.FieldTheory.Separable","name":"Polynomial.separable_prod_X_sub_C_iff"},{"module":"Mathlib.Algebra.Polynomial.Basic","name":"Polynomial.smulZeroClass"},{"module":"Mathlib.Algebra.Polynomial.Coeff","name":"Polynomial.smul_eq_C_mul"},{"module":"Mathlib.Analysis.LocallyConvex.WithSeminorms","name":"PolynormableSpace.continuousSMul"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Basic","name":"PosMulReflectLE.toPosMulReflectLT"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Defs","name":"PosMulReflectLT"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Basic","name":"PosMulStrictMono.toPosMulMono"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Defs",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et.finite_range"},{"module":"Mathlib.Order.SetNotation","name":"Set.iInter"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iInter_congr_Prop"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iInter_iInter_eq_or_left"},{"module":"Mathlib.Data.Set.Lattice.Bounded","name":"Set.iInter_of_empty"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iInter_subset"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iInter_true"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iInter_univ"},{"module":"Mathlib.Order.SetNotation","name":"Set.iUnion"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.iUnion_subset"},{"module":"Mathlib.Data.Set.Defs","name":"Set.image"},{"module":"Mathlib.Data.Set.Operations","name":"Set.image2"},{"module":"Mathlib.Data.Set.Image","name":"Set.image_comp"},{"module":"Mathlib.Data.Set.Image","name":"Set.image_mono"},{"module":"Mathlib.Data.Set.Image","name":"Set.image_univ"},{"module":"Mathlib.Data.Set.Inclusion","name":"Set.inclusion"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator.eq_1"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator_apply_eq_zero._simp_1"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator_empty"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator_of_mem"},{"module":"Mathlib.Algebra.Notation.Indicator","name":"Set.indicator_of_notMem"},{"module":"Mathlib.Data.Set.Finite.Basic","name":"Set.infinite_range_of_injective"},{"module":"Mathlib.Data.Set.Basic","name":"Set.instBoundedOrder"},{"module":"Mathlib.Data.Set.Operations","name":"Set.instCompl"},{"module":"Mathlib.Data.Set.BooleanAlgebra","name":"Set.instCompleteAtomicBooleanAlgebra"},{"module":"Mathlib.Data.Set.Basic","name":"Set.instDistribLattice"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instEmptyCollection"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instInsert"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instInter"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instLE"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instMembership"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instSDiff"},{"module":"Mathlib.Data.Set.Operations","name":"Set.instSProd"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instSingletonSet"},{"module":"Mathlib.Data.Set.Defs","name":"Set.instUnion"},{"module":"Mathlib.Data.Set.Basic","name":"Set.inter_comm"},{"module":"Mathlib.Data.Set.Basic","name":"Set.inter_eq_left"},{"module":"Mathlib.Data.Set.Basic","name":"Set.inter_subset_left"},{"module":"Mathlib.Data.Set.Basic","name":"Set.inter_subset_right"},{"module":"Mathlib.Data.Set.Basic","name":"Set.inter_union_distrib_left"},{"module":"Mathlib.Order.Interval.Set.Basic","name":"Set.left_mem_Icc"},{"module":"Mathlib.Order.Interval.Set.UnorderedInterval","name":"Set.left_mem_uIcc"},{"module":"Mathlib.Data.Set.Function","name":"Set.mapsTo_univ_iff"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Icc"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Icc._simp_1"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ici"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ici._simp_1"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ico"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Iic"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Iic._simp_2"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Iio._simp_2"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ioc._simp_1"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ioi"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ioi._simp_1"},{"module":"Mathlib.Order.Interval.Set.Defs","name":"Set.mem_Ioo._simp_1"},{"module":"Mathlib.Algebra.Group.Pointwise.Set.Basic","name":"Set.mem_add"},{"module":"Mathlib.Data.Set.Operations","name":"Set.mem_compl_iff"},{"module":"Mathlib.Data.Set.Operations","name":"Set.mem_compl_iff._simp_1"},{"module":"Mathlib.Data.Set.Basic","name":"Set.mem_empty_iff_false"},{"module":"Mathlib.Data.Set.Basic","name":"Set.mem_empty_iff_false._simp_1"},{"module":"Mathlib.Algebra.Group.Pointwise.Set.BigOperators","name":"Set.mem_fintype_prod"},{"module":"Mathlib.Order.SetNotation","name":"Set.mem_iInter"},{"module":"Mathlib.Order.SetNotation","name":"Set.mem_iInter._simp_1"},{"module":"Mathlib.Order.SetNotation","name":"Set.mem_iUnion"},{"module":"Mathlib.Order.SetNotation","name":"Set.mem_iUnion._simp_1"},{"module":"Mathlib.Data.Set.Lattice.Indexed","name":"Set.mem_iUnion_of_mem"},{"module":"Mathlib.Data.Set.Operations","name":"Set.mem_image._simp_1"},{"module":"Mathlib.Data.Set.Operations","name":"Set.mem_image_of_mem"},{"module":"Mathlib.Data.Set.Insert","name":"Set.mem_insert_iff._simp_1"},{"module":"Mathlib.Data.Set.Basic","name":"Set.mem_inter"},{"module":"Mathlib.Data.Set.Basic","name":"Set.mem_inter_iff"},{"module":"Mathlib.Data.Set.Basic","nam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_of_deriv_deriv_pos"},{"module":"Mathlib.Order.BoundedOrder.Basic","name":"isMax_iff_eq_top._simp_2"},{"module":"Mathlib.RingTheory.Noetherian.Basic","name":"isNoetherian_of_isNoetherianRing_of_finite"},{"module":"Mathlib.RingTheory.Noetherian.Basic","name":"isNoetherian_pi'"},{"module":"Mathlib.RingTheory.Noetherian.Basic","name":"isNoetherian_prod"},{"module":"Mathlib.Topology.Order.OrderClosed","name":"isOpen_Iio"},{"module":"Mathlib.Topology.Order.OrderClosed","name":"isOpen_Ioi"},{"module":"Mathlib.Topology.Order.OrderClosed","name":"isOpen_Ioo"},{"module":"Mathlib.Topology.Basic","name":"isOpen_biInter_finset"},{"module":"Mathlib.Topology.Separation.Basic","name":"isOpen_compl_singleton"},{"module":"Mathlib.Topology.Basic","name":"isOpen_empty"},{"module":"Mathlib.Topology.Basic","name":"isOpen_empty._simp_1"},{"module":"Mathlib.Topology.Basic","name":"isOpen_iUnion"},{"module":"Mathlib.Topology.Neighborhoods","name":"isOpen_iff_mem_nhds"},{"module":"Mathlib.Topology.Closure","name":"isOpen_interior"},{"module":"Mathlib.Topology.Order.OrderClosed","name":"isOpen_lt"},{"module":"Mathlib.Topology.Separation.Hausdorff","name":"isOpen_ne_fun"},{"module":"Mathlib.Topology.Defs.Basic","name":"isOpen_univ"},{"module":"Mathlib.Topology.Connected.PathConnected","name":"isPathConnected_iff"},{"module":"Mathlib.MeasureTheory.MeasurableSpace.Prod","name":"isPiSystem_prod"},{"module":"Mathlib.Topology.Connected.Basic","name":"isPreconnected_iff_preconnectedSpace"},{"module":"Mathlib.Algebra.GroupWithZero.Basic","name":"isReduced_of_noZeroDivisors"},{"module":"Mathlib.Analysis.InnerProductSpace.Adjoint","name":"isSelfAdjoint_starProjection"},{"module":"Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital","name":"isUnit_cfc_iff"},{"module":"Mathlib.Algebra.GroupWithZero.Units.Basic","name":"isUnit_iff_ne_zero"},{"module":"Mathlib.Algebra.GroupWithZero.Units.Basic","name":"isUnit_iff_ne_zero._simp_1"},{"module":"Mathlib.Analysis.Calculus.MeanValue","name":"is_const_of_fderiv_eq_zero"},{"module":"Mathlib.Topology.MetricSpace.Isometry","name":"isometry_iff_dist_eq"},{"module":"Init.Prelude","name":"ite"},{"module":"Init.Data.NeZero","name":"ite.congr_simp"},{"module":"Mathlib.Basic.Logic.Basic","name":"ite_apply"},{"module":"Init.SimpLemmas","name":"ite_congr"},{"module":"Init.Core","name":"ite_eq_left"},{"module":"Init.SimpLemmas","name":"ite_eq_left_of_eq_true"},{"module":"Init.Core","name":"ite_eq_right"},{"module":"Init.PropLemmas","name":"ite_eq_right_iff"},{"module":"Init.PropLemmas","name":"ite_eq_right_iff._simp_1"},{"module":"Init.SimpLemmas","name":"ite_eq_right_of_eq_false"},{"module":"Init.SimpLemmas","name":"ite_false"},{"module":"Mathlib.Algebra.Notation.Defs","name":"ite_mul"},{"module":"Mathlib.Algebra.Group.Basic","name":"ite_pow"},{"module":"Init.SimpLemmas","name":"ite_self"},{"module":"Mathlib.Algebra.Group.Basic","name":"ite_smul"},{"module":"Init.SimpLemmas","name":"ite_true"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDeriv"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDerivWithin"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDerivWithin_eq_iteratedDeriv"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas","name":"iteratedDeriv_const_mul"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDeriv_one"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas","name":"iteratedDeriv_sub"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDeriv_succ"},{"module":"Mathlib.Analysis.Calculus.IteratedDeriv.Defs","name":"iteratedDeriv_zero"},{"module":"Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries","name":"iteratedFDeriv"},{"module":"Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries","name":"iteratedFDeriv_one_apply"},{"module":"Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries","name":"iteratedFDeriv_two_apply"},{"module":"Mathlib.Algebra.Order.Group.Unbundled.Abs","name":"le_abs_self"},{"module":"Mathlib.Algebra.Order.Monoid.Unbundled.Basic","name":"le_add_iff_nonneg_left._simp_1"},{"module":"Mathlib.Algebra.Order.Monoid.Unbundled.Basic","name":"le_add_iff_nonneg_right._simp_1"},{"module":"Mathlib.Algebra.Order.Monoid.Unbundled.Basic","name":"le_add_of_nonneg_left"},{"module":"Mathlib.Algebra.Order.Monoid.Unbundled.Basic","name":"le_add_of_nonneg_right"},{"module":"Mathlib.Order.Defs.PartialOrder","name":"le_antisymm"},{"module":"Mathlib.Order.ConditionallyCompleteLattice.Basic","name":"le_csInf"},{"module":"Mathlib.Order.ConditionallyCompleteLattice.Basic","name":"le_csSup"},{"module":"Mathlib.Algebra.Order.GroupWithZero.Basic","name":"le_div_iff\u2080"},{"module":"Mathlib.Order.CompleteLattice.Basic","name":"le_iSup"},{"module":"Mathlib.Order.CompleteLattice.Basic","name":"le_iSup_of_le"},{"module":"Mathlib.Order.Lattice","name":"le_inf_iff._simp_1"},{"module":"Mathlib.Order.Defs.LinearOrder","name":"le_max_iff._simp_1"},{"module":"Mathlib.Order.De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oincare.Analysis.BrownianStoppingExitHamiltonianPrefix","GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianRestrictedVolterra","GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianStoppedAdaptation","GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianStoppedEquation","GinibrePoincare.Analysis.BrownianStoppingExitHamiltonianStoppedPath","GinibrePoincare.Analysis.BrownianStoppingExitLifetimeStopping","GinibrePoincare.Analysis.BrownianStoppingExitLimit","GinibrePoincare.Analysis.BrownianStoppingExitLyapunov","GinibrePoincare.Analysis.BrownianStoppingExitMartingale","GinibrePoincare.Analysis.BrownianStoppingExitMaximalAdaptation","GinibrePoincare.Analysis.BrownianStoppingExitMaximalEquation","GinibrePoincare.Analysis.BrownianStoppingExitNoisePath","GinibrePoincare.Analysis.BrownianStoppingExitPastNoisePath","GinibrePoincare.Analysis.CenterOfMassEigenfunctions","GinibrePoincare.Analysis.CollisionNull","GinibrePoincare.Analysis.CompactLipschitzLSIExtension","GinibrePoincare.Analysis.ComplexGaussianDensity","GinibrePoincare.Analysis.ComplexGaussianIntegrationByParts","GinibrePoincare.Analysis.ComplexGaussianMoments","GinibrePoincare.Analysis.ComplexGaussianProductIntegral","GinibrePoincare.Analysis.ComplexGeneratorCalculus","GinibrePoincare.Analysis.ComplexHermite","GinibrePoincare.Analysis.ComplexHermiteLowering","GinibrePoincare.Analysis.ComplexHermiteOrthogonality","GinibrePoincare.Analysis.ComplexSquaredGradient","GinibrePoincare.Analysis.CorrespondenceAlgebraCenterCovariance","GinibrePoincare.Analysis.CorrespondenceAlgebraGenerator","GinibrePoincare.Analysis.CorrespondenceAlgebraQuadratic","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCapacitySpeed","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenFundamental","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenHomotopy","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenIBP","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenKernel","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenLimit","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenParametric","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenParametricHomotopy","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenPotential","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenRegularized","GinibrePoincare.Analysis.CorrespondenceAuxiliaryCauchyGreenSmoothSolver","GinibrePoincare.Analysis.CorrespondenceAuxiliaryDbarLargeNorm","GinibrePoincare.Analysis.CorrespondenceAuxiliaryEntireAnalytic","GinibrePoincare.Analysis.CorrespondenceAuxiliaryEntireCRTests","GinibrePoincare.Analysis.CorrespondenceAuxiliaryEqualityAnalytic","GinibrePoincare.Analysis.CorrespondenceAuxiliaryFirstModeSeries","GinibrePoincare.Analysis.CorrespondenceAuxiliaryGeneratorVectorMeasure","GinibrePoincare.Analysis.CorrespondenceAuxiliaryGinibreVectorMeasure","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteDegreeOrder","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteGramSchmidt","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteLeading","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHermiteRectangleL2","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHolomorphicDerivative","GinibrePoincare.Analysis.CorrespondenceAuxiliaryHolomorphicFormalSeries","GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointCauchyRiemann","GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointMollification","GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointRadialKernel","GinibrePoincare.Analysis.CorrespondenceAuxiliaryJointWeyl","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeault","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultApproximation","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundary","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultBoundaryIteration","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultConfiguration","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultCoordinate","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultDifferential","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultHomotopy","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIBP","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultInterior","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultIteration","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpBall","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultLpIteration","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultMollification","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultOne","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultSmooth","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedCorrespondence","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncatedIteration","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultTruncation","GinibrePoincare.Analysis.CorrespondenceAuxiliaryLocalDolbeaultWeakLimit","GinibrePoincare.Analysis.CorrespondenceAuxiliaryMonomialMultilinear","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPolynomialExamples","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveGeneratorMeasure","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightClosure","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightLocal","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightPairing","GinibrePoincare.Analysis.CorrespondenceAuxiliaryPositiveWeightUniform","GinibrePoincare.Analysis.CorrespondenceAuxiliaryQuadraticGenerator","GinibrePoincare.Analysis.CorrespondenceAuxiliaryQuadraticNonPolynomial","GinibrePoincare.Analysis.CorrespondenceAuxiliarySeriesDerivative","GinibrePoincare.Analysis.CorrespondenceAuxiliarySlaterGroundState","GinibrePoincare.Analysis.CorrespondenceAuxiliarySlaterLabels","GinibrePoincare.Analysis.CorrespondenceAuxiliaryTensorExpansion","GinibrePoincare.Analysis.CorrespondenceAuxiliaryTensorGramSchmidt","GinibrePoincare.Analysis.CorrespondenceAuxiliaryTriangularGramSchmidt","GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSemigroupRepresentation","GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorSpectralMeasure","GinibrePoincare.Analysis.CorrespondenceAuxiliaryVectorZeroAtom","GinibrePoincare.Analysis.CorrespondenceBrascampLieb","GinibrePoincare.Analysis.CorrespondenceBrascampLiebAdjoint","GinibrePoincare.Analysis.CorrespondenceBrascampLiebBochner","GinibrePoincare.Analysis.CorrespondenceBrascampLiebBochnerIntegral","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCenter","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCompactBound","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCompactEnergy","GinibrePoincare.Analysis.CorrespondenceBrascampLiebConstants","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCore","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCoreDual","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCoreRange","GinibrePoincare.Analysis.CorrespondenceBrascampLiebCutoffs","GinibrePoincare.Analysis.CorrespondenceBrascampLiebDense","GinibrePoincare.Analysis.CorrespondenceBrascampLiebDensityGenerator","GinibrePoincare.Analysis.CorrespondenceBrascampLiebDuality","GinibrePoincare.Analysis.CorrespondenceBrascampLiebGibbs","GinibrePoincare.Analysis.CorrespondenceBrascampLiebHessian","GinibrePoincare.Analysis.CorrespondenceBrascampLiebIntegralCS","GinibrePoincare.Analysis.CorrespondenceBrascampLiebJets","GinibrePoincare.Analysis.CorrespondenceBrascampLiebLinear","GinibrePoincare.Analysis.CorrespondenceBrascampLiebLipschitz","GinibrePoincare.Analysis.CorrespondenceBrascampLiebLocalL2","GinibrePoincare.Analysis.CorrespondenceBrascampLiebMass","GinibrePoincare.Analysis.CorrespondenceBrascampLiebMatrix","GinibrePoincare.Analysis.CorrespondenceBrascampLiebScalar","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeak","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakAdjoint","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakBound","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakDirichlet","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakDual","GinibrePoincare.Analysis.CorrespondenceBrascampLiebWeakTests","GinibrePoincare.Analysis.CorrespondenceCollisionCoordinates","GinibrePoincare.Analysis.CorrespondenceCollisionCutoff","GinibrePoincare.Analysis.CorrespondenceCollisionDensity","GinibrePoincare.Analysis.CorrespondenceCollisionMass","GinibrePoincare.Analysis.CorrespondenceCollisionProduct","GinibrePoincare.Analysis.CorrespondenceCollisionProductRates","GinibrePoincare.Analysis.CorrespondenceCollisionRates","GinibrePoincare.Analysis.CorrespondenceCollisionSupport","GinibrePoincare.Analysis.CorrespondenceCollisionVolume","GinibrePoincare.Analysis.CorrespondenceCurvatureComplexHessian","GinibrePoincare.Analysis.CorrespondenceCurvatureDeficit","GinibrePoincare.Analysis.CorrespondenceCurvatureGradient","GinibrePoincare.Analysis.CorrespondenceCurvatureHessian","GinibrePoincare.Analysis.CorrespondenceCurvatureLinear","GinibrePoincare.Analysis.CorrespondenceCurvatureNegativeTest","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoung","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungInverse","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungInverseFubini","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungInverseSlice","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungKernel","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMollifier","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMollifierPairing","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplier","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungMultiplierComposition","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungPairing","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungSmooth","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungSmoothGeometry","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungSmoothLocal","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungSmoothPairing","GinibrePoincare.Analysis.CorrespondenceDolbeaultYoungTranslation","GinibrePoincare.Analysis.CorrespondenceDynamicsAlmostSureStopping","GinibrePoincare.Analysis.CorrespondenceDynamicsBrownianStrongMarkov","GinibrePoincare.Analysis.CorrespondenceDynamicsConstantLawLimit","GinibrePoincare.Analysis.CorrespondenceDynamicsGlobalCIR","GinibrePoincare.Analysis.CorrespondenceDynamicsHunt","GinibrePoincare.Analysis.CorrespondenceDynamicsLocalization","GinibrePoincare.Analysis.CorrespondenceDynamicsNoiseShift","GinibrePoincare.Analysis.CorrespondenceDynamicsRestart","GinibrePoincare.Analysis.CorrespondenceDynamicsStoppedNoiseIndependence","GinibrePoincare.Analysis.CorrespondenceDynamicsStoppedPast","GinibrePoincare.Analysis.CorrespondenceDynamicsStoppingCountable","GinibrePoincare.Analysis.CorrespondenceDynamicsStoppingFinite","GinibrePoincare.Analysis.CorrespondenceDynamicsStoppingOptional","GinibrePoincare.Analysis.CorrespondenceDynamicsStrongMarkov","GinibrePoincare.Analysis.CorrespondenceGUEBarrier","GinibrePoincare.Analysis.CorrespondenceGUEBoundedLSI","GinibrePoincare.Analysis.CorrespondenceGUEC1H1Membership","GinibrePoincare.Analysis.CorrespondenceGUECenterGaussian","GinibrePoincare.Analysis.CorrespondenceGUECenterGeometry","GinibrePoincare.Analysis.CorrespondenceGUECenterIntegrals","GinibrePoincare.Analysis.CorrespondenceGUECenterSplit","GinibrePoincare.Analysis.CorrespondenceGUECenterWitness","GinibrePoincare.Analysis.CorrespondenceGUEChamberIntegrals","GinibrePoincare.Analysis.CorrespondenceGUEChamberPartition","GinibrePoincare.Analysis.CorrespondenceGUEConvexity","GinibrePoincare.Analysis.CorrespondenceGUEDensityConvergence","GinibrePoincare.Analysis.CorrespondenceGUEDoubledLSI","GinibrePoincare.Analysis.CorrespondenceGUEEndpoints","GinibrePoincare.Analysis.CorrespondenceGUEExpectationConvergence","GinibrePoincare.Analysis.CorrespondenceGUEFullMeasure","GinibrePoincare.Analysis.CorrespondenceGUEGeometry","GinibrePoincare.Analysis.CorrespondenceGUEH1Closure","GinibrePoincare.Analysis.CorrespondenceGUELSIWitness","GinibrePoincare.Analysis.CorrespondenceGUEMarginalIntegrals","GinibrePoincare.Analysis.CorrespondenceGUENormalization","GinibrePoincare.Analysis.CorrespondenceGUEOptimality","GinibrePoincare.Analysis.CorrespondenceGUEOrderedDensity","GinibrePoincare.Analysis.CorrespondenceGUEOrderedLSI","GinibrePoincare.Analysis.CorrespondenceGUEPaperH1","GinibrePoincare.Analysis.CorrespondenceGUEPermutationGradient","GinibrePoincare.Analysis.CorrespondenceGUEPermutationMeasure","GinibrePoincare.Analysis.CorrespondenceGUEProjection","GinibrePoincare.Analysis.CorrespondenceGUERealLSI","GinibrePoincare.Analysis.CorrespondenceGUERealMeasure","GinibrePoincare.Analysis.CorrespondenceGUERealPoincare","GinibrePoincare.Analysis.CorrespondenceGUERegularizedLimit","GinibrePoincare.Analysis.CorrespondenceGUERegularizedPotential","GinibrePoincare.Analysis.CorrespondenceGUESmoothAveraging","GinibrePoincare.Analysis.CorrespondenceGUESobolevAveraging","GinibrePoincare.Analysis.CorrespondenceGUESpatialApproximation","GinibrePoincare.Analysis.CorrespondenceGUESplitDensity","GinibrePoincare.Analysis.CorrespondenceGUESplitVolume","GinibrePoincare.Analysis.CorrespondenceGUESymmetricCutoff","GinibrePoincare.Analysis.CorrespondenceGUESymmetricH1Closure","GinibrePoincare.Analysis.CorrespondenceGUESymmetricInequalities","GinibrePoincare.Analysis.CorrespondenceGUESymmetricSpatialApproximation","GinibrePoincare.Analysis.CorrespondenceLogApproximation","GinibrePoincare.Analysis.CorrespondenceLogDistribution","GinibrePoincare.Analysis.CorrespondenceLogIntegrability","GinibrePoincare.Analysis.CorrespondenceLogKernel","GinibrePoincare.Analysis.CorrespondenceLogLimit","GinibrePoincare.Analysis.CorrespondenceLogRadial","GinibrePoincare.Analysis.CorrespondenceLogRegularized","GinibrePoincare.Analysis.CorrespondenceLogWeakDerivative","GinibrePoincare.Analysis.CorrespondenceMatrixWeakClosure","GinibrePoincare.Analysis.CorrespondenceOperatorCfcEigenvector","GinibrePoincare.Analysis.CorrespondenceOperatorComplex","GinibrePoincare.Analysis.CorrespondenceOperatorComplexHermiteMultiplier","GinibrePoincare.Analysis.CorrespondenceOperatorConnected","GinibrePoincare.Analysis.CorrespondenceOperatorConservation","GinibrePoincare.Analysis.CorrespondenceOperatorCoreGreen","GinibrePoincare.Analysis.CorrespondenceOperatorErgodicClosure","GinibrePoincare.Analysis.CorrespondenceOperatorErgodicScalar","GinibrePoincare.Analysis.CorrespondenceOperatorErgodicity","GinibrePoincare.Analysis.CorrespondenceOperatorEvolution","GinibrePoincare.Analysis.CorrespondenceOperatorFixedSpace","GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRoot","GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootCalculus","GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootForm","GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootGraph","GinibrePoincare.Analysis.CorrespondenceOperatorFriedrichsSquareRootRange","GinibrePoincare.Analysis.CorrespondenceOperatorGreen","GinibrePoincare.Analysis.CorrespondenceOperatorHermiteMultiplier","GinibrePoincare.Analysis.CorrespondenceOperatorInvariantDensity","GinibrePoincare.Analysis.CorrespondenceOperatorInvariantIntegral","GinibrePoincare.Analysis.CorrespondenceOperatorInvariantLimit","GinibrePoincare.Analysis.CorrespondenceOperatorInvariantUniqueness","GinibrePoincare.Analysis.CorrespondenceOperatorKilledAbsoluteContinuity","GinibrePoincare.Analysis.CorrespondenceOperatorLocalMartingaleProblem","GinibrePoincare.Analysis.CorrespondenceOperatorLocality","GinibrePoincare.Analysis.CorrespondenceOperatorMarkov","GinibrePoincare.Analysis.CorrespondenceOperatorMartingaleApproximation","GinibrePoincare.Analysis.CorrespondenceOperatorMartingaleProblem","GinibrePoincare.Analysis.CorrespondenceOperatorNumberBochnerClosure","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCfc","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCfcRoot","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCore","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreCauchy","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreCutoff","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactCoreJets","GinibrePoincare.Analysis.CorrespondenceOperatorNumberCompactGraph","GinibrePoincare.Analysis.CorrespondenceOperatorNumberDomain","GinibrePoincare.Analysis.CorrespondenceOperatorNumberFiniteForm","GinibrePoincare.Analysis.CorrespondenceOperatorNumberForm","GinibrePoincare.Analysis.CorrespondenceOperatorNumberFormDomain","GinibrePoincare.Analysis.CorrespondenceOperatorNumberInverse","GinibrePoincare.Analysis.CorrespondenceOperatorNumberInverseRoot","GinibrePoincare.Analysis.CorrespondenceOperatorNumberKernel","GinibrePoincare.Analysis.CorrespondenceOperatorNumberResolvent","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSecondBounds","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSelfAdjoint","GinibrePoincare.Analysis.CorrespondenceOperatorNumberShiftedRoot","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralGraph","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralResolvent","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectralSelfAdjoint","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSpectrum","GinibrePoincare.Analysis.CorrespondenceOperatorNumberSquareRoot","GinibrePoincare.Analysis.CorrespondenceOperatorNumberTransfer","GinibrePoincare.Analysis.CorrespondenceOperatorNumberWeakDomain","GinibrePoincare.Analysis.CorrespondenceOperatorOUSmoothing","GinibrePoincare.Analysis.CorrespondenceOperatorOrbits","GinibrePoincare.Analysis.CorrespondenceOperatorRealErgodicity","GinibrePoincare.Analysis.CorrespondenceOperatorRealEvolution","GinibrePoincare.Analysis.CorrespondenceOperatorRegularity","GinibrePoincare.Analysis.CorrespondenceOperatorResolvent","GinibrePoincare.Analysis.CorrespondenceOperatorSemigroupComparison","GinibrePoincare.Analysis.CorrespondenceOperatorSmoothCore","GinibrePoincare.Analysis.CorrespondenceOperatorSmoothIdentification","GinibrePoincare.Analysis.CorrespondenceOperatorStochasticResolvent","GinibrePoincare.Analysis.CorrespondenceOperatorStochasticSemigroup","GinibrePoincare.Analysis.CorrespondenceOperatorStoppedMartingale","GinibrePoincare.Analysis.CorrespondenceOperatorUnrestrictedGamma","GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradient","GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientLocal","GinibrePoincare.Analysis.CorrespondenceOperatorZeroGradientMollifier","GinibrePoincare.Analysis.CorrespondencePolynomialCoulomb","GinibrePoincare.Analysis.CorrespondencePolynomialDifferential","GinibrePoincare.Analysis.CorrespondencePolynomialDomain","GinibrePoincare.Analysis.CorrespondencePolynomialGaussian","GinibrePoincare.Analysis.CorrespondencePolynomialGeneratorL2","GinibrePoincare.Analysis.CorrespondencePolynomialLipschitz","GinibrePoincare.Analysis.CorrespondencePolynomialNormalization","GinibrePoincare.Analysis.CorrespondencePolynomialRealGaussian","GinibrePoincare.Analysis.CorrespondencePolynomialRealGaussianDensity","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticC1Tests","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticConvolution","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticCutoffEnergy","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticCutoffForm","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticCutoffGradient","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticDensity","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticDivision","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticEquation","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticFormTesting","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticGreen","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticLiouville","GinibrePoincare.Analysis.CorrespondenceWeightedEllipticLocalSobolev","GinibrePoincare.Analysis.Correspondenc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ibrePoincare.Analysis.GaussianRadialLift","GinibrePoincare.Analysis.GaussianSobolevApproximation","GinibrePoincare.Analysis.GaussianVandermondePhase","GinibrePoincare.Analysis.GeneralPotentialAlternatedPhaseClassification","GinibrePoincare.Analysis.GeneralPotentialCenteredMean","GinibrePoincare.Analysis.GeneralPotentialCenteringDecomposition","GinibrePoincare.Analysis.GeneralPotentialCompactGap","GinibrePoincare.Analysis.GeneralPotentialCompactLift","GinibrePoincare.Analysis.GeneralPotentialLpConjugation","GinibrePoincare.Analysis.GeneralPotentialNonnegativePhaseGeometry","GinibrePoincare.Analysis.GeneralPotentialPositivePhaseClosure","GinibrePoincare.Analysis.GeneralPotentialPositivePhaseGeometry","GinibrePoincare.Analysis.GeneralPotentialProjectionGeometry","GinibrePoincare.Analysis.GeneralPotentialProjectionOrthogonal","GinibrePoincare.Analysis.GeneralPotentialProjectionPermutation","GinibrePoincare.Analysis.GeneralPotentialProjectionPhase","GinibrePoincare.Analysis.GeneralPotentialProjectionRealVariance","GinibrePoincare.Analysis.GeneralPotentialQuotientAlternatingClosure","GinibrePoincare.Analysis.GeneralPotentialQuotientCentering","GinibrePoincare.Analysis.GeneralPotentialQuotientCompactGap","GinibrePoincare.Analysis.GeneralPotentialQuotientNonnegativeClosure","GinibrePoincare.Analysis.GeneralPotentialQuotientProjection","GinibrePoincare.Analysis.GeneralPotentialQuotientVariance","GinibrePoincare.Analysis.GeneralPotentialSharpPoincare","GinibrePoincare.Analysis.GeneralPotentialVandermondeCentered","GinibrePoincare.Analysis.GeneralPotentialVandermondeDensity","GinibrePoincare.Analysis.GeneralPotentialVandermondeEnergy","GinibrePoincare.Analysis.GeneralPotentialVandermondeGauge","GinibrePoincare.Analysis.GeneralPotentialVandermondeInverse","GinibrePoincare.Analysis.GeneralPotentialVandermondeL2","GinibrePoincare.Analysis.GeneralPotentialVandermondePhase","GinibrePoincare.Analysis.GeneralPotentialVandermondeSymmetry","GinibrePoincare.Analysis.GeneralPotentialWeightedPolynomialPhase","GinibrePoincare.Analysis.GeneralRadialProjectionCharacters","GinibrePoincare.Analysis.GeneralRadialProjectionFourier","GinibrePoincare.Analysis.GeneralRadialProjectionModes","GinibrePoincare.Analysis.GeneralRadialProjectionMonomials","GinibrePoincare.Analysis.GeneralRadialProjectionNegative","GinibrePoincare.Analysis.GeneralRadialProjectionPhase","GinibrePoincare.Analysis.GeneralizedLaguerre","GinibrePoincare.Analysis.GinibreArbitraryWeakPairApproximation","GinibrePoincare.Analysis.GinibreArbitraryWeakPairClosure","GinibrePoincare.Analysis.GinibreBrownianIntegralApproximationTransfer","GinibrePoincare.Analysis.GinibreBrownianIntegralBaseMartingale","GinibrePoincare.Analysis.GinibreBrownianIntegralCoefficientMesh","GinibrePoincare.Analysis.GinibreBrownianIntegralConditional","GinibrePoincare.Analysis.GinibreBrownianIntegralContinuous","GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialApproximation","GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialDensity","GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialLimit","GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialMeasure","GinibrePoincare.Analysis.GinibreBrownianIntegralExponentialNatural","GinibrePoincare.Analysis.GinibreBrownianIntegralFourErrorBound","GinibrePoincare.Analysis.GinibreBrownianIntegralFrozenConditional","GinibrePoincare.Analysis.GinibreBrownianIntegralFrozenMartingale","GinibrePoincare.Analysis.GinibreBrownianIntegralFrozenStep","GinibrePoincare.Analysis.GinibreBrownianIntegralHorizon","GinibrePoincare.Analysis.GinibreBrownianIntegralHorizonComparison","GinibrePoincare.Analysis.GinibreBrownianIntegralInitialCutoff","GinibrePoincare.Analysis.GinibreBrownianIntegralInitialIntervalBound","GinibrePoincare.Analysis.GinibreBrownianIntegralIntervalConvergence","GinibrePoincare.Analysis.GinibreBrownianIntegralIntervalIsometry","GinibrePoincare.Analysis.GinibreBrownianIntegralIsometry","GinibrePoincare.Analysis.GinibreBrownianIntegralL2Completion","GinibrePoincare.Analysis.GinibreBrownianIntegralL2Limit","GinibrePoincare.Analysis.GinibreBrownianIntegralLimitAdaptation","GinibrePoincare.Analysis.GinibreBrownianIntegralLimitIdentification","GinibrePoincare.Analysis.GinibreBrownianIntegralLimitTransfer","GinibrePoincare.Analysis.GinibreBrownianIntegralLinear","GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleCap","GinibrePoincare.Analysis.GinibreBrownianIntegralMartingaleLimit","GinibrePoincare.Analysis.GinibreBrownianIntegralMeanSquareCauchy","GinibrePoincare.Analysis.GinibreBrownianIntegralPartialCauchy","GinibrePoincare.Analysis.GinibreBrownianIntegralPartialGeometry","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedAggregate","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedApproximation","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedCauchy","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedContinuous","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedPartialApproximation","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedPartialBound","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedPartialContinuous","GinibrePoincare.Analysis.GinibreBrownianIntegralPuncturedSubstitution","GinibrePoincare.Analysis.GinibreBrownianIntegralRefinementBound","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitution","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionDiagonal","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionError","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionFinite","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionMesh","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionNatural","GinibrePoincare.Analysis.GinibreBrownianIntegralSubstitutionRefinement","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltActualCanonicalLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltCanonicalAudit","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltCanonicalMap","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltCanonicalPathMeasure","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltConfigurationLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltContinuousLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltDensityTest","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltEndpoint","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltFiniteLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltJointCanonicalPath","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltKilledMapping","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltKilledOriginalLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUAudit","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUReference","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUStopped","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUSublevel","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUSublevelCanonicalLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltOUSurvival","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltPathLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltRationalLaw","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltTestLimit","GinibrePoincare.Analysis.GinibreBrownianIntegralTiltVolterra","GinibrePoincare.Analysis.GinibreBrownianIntegralUniformLimit","GinibrePoincare.Analysis.GinibreBrownianIntegralUniformSums","GinibrePoincare.Analysis.GinibreBrownianIntegralVanishingAmplitude","GinibrePoincare.Analysis.GinibreBrownianProjection","GinibrePoincare.Analysis.GinibreC1WeakPoincare","GinibrePoincare.Analysis.GinibreCenterProjectionClasses","GinibrePoincare.Analysis.GinibreCenterProjectionEquality","GinibrePoincare.Analysis.GinibreCenterProjectionGaussian","GinibrePoincare.Analysis.GinibreCollisionCapacity","GinibrePoincare.Analysis.GinibreCollisionCutoff","GinibrePoincare.Analysis.GinibreCollisionCutoffEnergy","GinibrePoincare.Analysis.GinibreCollisionCutoffSobolevApproximation","GinibrePoincare.Analysis.GinibreComplexCoreClosureEquivalence","GinibrePoincare.Analysis.GinibreComplexProjectionGeometry","GinibrePoincare.Analysis.GinibreConjugationGeometry","GinibrePoincare.Analysis.GinibreDensityBound","GinibrePoincare.Analysis.GinibreDirectionalCoordinates","GinibrePoincare.Analysis.GinibreDistributionalClosure","GinibrePoincare.Analysis.GinibreDistributionalGradient","GinibrePoincare.Analysis.GinibreDrivenPathBrownianQuadraticControl","GinibrePoincare.Analysis.GinibreDrivenPathCenterFormula","GinibrePoincare.Analysis.GinibreDrivenPathClippedLocalFlow","GinibrePoincare.Analysis.GinibreDrivenPathClosedHittingTime","GinibrePoincare.Analysis.GinibreDrivenPathCompactClippedFlow","GinibrePoincare.Analysis.GinibreDrivenPathCompactClosedEquation","GinibrePoincare.Analysis.GinibreDrivenPathCompactContinuation","GinibrePoincare.Analysis.GinibreDrivenPathCompactExtension","GinibrePoincare.Analysis.GinibreDrivenPathCompactLocalFlow","GinibrePoincare.Analysis.GinibreDrivenPathCompactRestart","GinibrePoincare.Analysis.GinibreDrivenPathContinuousLocalFlow","GinibrePoincare.Analysis.GinibreDrivenPathContinuousNoisePicard","GinibrePoincare.Analysis.GinibreDrivenPathDriftLeftSums","GinibrePoincare.Analysis.GinibreDrivenPathDriftRegularity","GinibrePoincare.Analysis.GinibreDrivenPathEscapeCriterion","GinibrePoincare.Analysis.GinibreDrivenPathFactorization","GinibrePoincare.Analysis.GinibreDrivenPathFlowNeighborhood","GinibrePoincare.Analysis.GinibreDrivenPathGinibreStability","GinibrePoincare.Analysis.GinibreDrivenPathLipschitzStability","GinibrePoincare.Analysis.GinibreDrivenPathLocalExistence","GinibrePoincare.Analysis.GinibreDrivenPathLocalStability","GinibrePoincare.Analysis.GinibreDrivenPathLocalUniqueness","GinibrePoincare.Analysis.GinibreDrivenPathMeasurableLocalFlow","GinibrePoincare.Analysis.GinibreDrivenPathNoiseClip","GinibrePoincare.Analysis.GinibreDrivenPathOU","GinibrePoincare.Analysis.GinibreDrivenPathOUItoSquare","GinibrePoincare.Analysis.GinibreDrivenPathOUProjection","GinibrePoincare.Analysis.GinibreDrivenPathOUQuadraticVariation","GinibrePoincare.Analysis.GinibreDrivenPathOUShift","GinibrePoincare.Analysis.GinibreDrivenPathOUUniqueness","GinibrePoincare.Analysis.GinibreDrivenPathOneParticleUniqueness","GinibrePoincare.Analysis.GinibreDrivenPathQuadraticCross","GinibrePoincare.Analysis.GinibreDrivenPathRestart","GinibrePoincare.Analysis.GinibreDrivenPathRiemann","GinibrePoincare.Analysis.GinibreDrivenPathRiemannConvergence","GinibrePoincare.Analysis.GinibreDrivenPathUniformLocalExistence","GinibrePoincare.Analysis.GinibreDrivenPathUniformPartition","GinibrePoincare.Analysis.GinibreDrivenPathVolterraUniqueness","GinibrePoincare.Analysis.GinibreDynamicsDrift","GinibrePoincare.Analysis.GinibreDynamicsGenerator","GinibrePoincare.Analysis.GinibreEntireProjectionBridge","GinibrePoincare.Analysis.GinibreEntireProjectionDistance","GinibrePoincare.Analysis.GinibreEntireProjectionEndpoints","GinibrePoincare.Analysis.GinibreEntireProjectionGeometry","GinibrePoincare.Analysis.GinibreEntropy","GinibrePoincare.Analysis.GinibreEqualityConjugateModeDetection","GinibrePoincare.Analysis.GinibreEqualityConjugatePolynomialDegree","GinibrePoincare.Analysis.GinibreEqualityConjugateProjection","GinibrePoincare.Analysis.GinibreEqualityCore","GinibrePoincare.Analysis.GinibreEqualityFiniteConjugateDegree","GinibrePoincare.Analysis.GinibreEqualityFirstQuotient","GinibrePoincare.Analysis.GinibreEqualityFullGenerator","GinibrePoincare.Analysis.GinibreEqualityMixedFactor","GinibrePoincare.Analysis.GinibreEqualityMixedHermite","GinibrePoincare.Analysis.GinibreEqualityMixedPolynomial","GinibrePoincare.Analysis.GinibreEqualityPolynomial","GinibrePoincare.Analysis.GinibreEqualityWeakAffine","GinibrePoincare.Analysis.GinibreEqualityWeakConjugateModes","GinibrePoincare.Analysis.GinibreEqualityWeakDeficit","GinibrePoincare.Analysis.GinibreEqualityWeakDegreeElimination","GinibrePoincare.Analysis.GinibreEqualityWeakHolomorphic","GinibrePoincare.Analysis.GinibreEqualityWeakLinear","GinibrePoincare.Analysis.GinibreEqualityWeakModes","GinibrePoincare.Analysis.GinibreEqualityWeakVariational","GinibrePoincare.Analysis.GinibreEquilibriumProcessStationarityJoint","GinibrePoincare.Analysis.GinibreEquilibriumProcessStationarityPath","GinibrePoincare.Analysis.GinibreFullGeneratorCenterEigenvectors","GinibrePoincare.Analysis.GinibreFullGeneratorComplexification","GinibrePoincare.Analysis.GinibreFullGeneratorCoreCompatibility","GinibrePoincare.Analysis.GinibreFullGeneratorCoreIdentification","GinibrePoincare.Analysis.GinibreFullGeneratorDbarTransform","GinibrePoincare.Analysis.GinibreFullGeneratorDeficit","GinibrePoincare.Analysis.GinibreFullGeneratorDensity","GinibrePoincare.Analysis.GinibreFullGeneratorEnergy","GinibrePoincare.Analysis.GinibreFullGeneratorHermiteLowering","GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialCompatibility","GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialGradient","GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialGraph","GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialIdentification","GinibrePoincare.Analysis.GinibreFullGeneratorPolynomialMoments","GinibrePoincare.Analysis.GinibreFullGeneratorResolvent","GinibrePoincare.Analysis.GinibreFullGeneratorSmoothIdentification","GinibrePoincare.Analysis.GinibreFullGeneratorSpectrum","GinibrePoincare.Analysis.GinibreFullGeneratorSymmetry","GinibrePoincare.Analysis.GinibreFullGeneratorVariational","GinibrePoincare.Analysis.GinibreFullGeneratorWeakSpace","GinibrePoincare.Analysis.GinibreFullSemigroup","GinibrePoincare.Analysis.GinibreFullSemigroupCFC","GinibrePoincare.Analysis.GinibreFullSemigroupChainRule","GinibrePoincare.Analysis.GinibreFullSemigroupConservation","GinibrePoincare.Analysis.GinibreFullSemigroupConstants","GinibrePoincare.Analysis.GinibreFullSemigroupDecay","GinibrePoincare.Analysis.GinibreFullSemigroupDeficitConsequences","GinibrePoincare.Analysis.GinibreFullSemigroupDifferentiability","GinibrePoincare.Analysis.GinibreFullSemigroupDynamics","GinibrePoincare.Analysis.GinibreFullSemigroupEigenvectors","GinibrePoincare.Analysis.GinibreFullSemigroupEulerCFC","GinibrePoincare.Analysis.GinibreFullSemigroupEulerMultiplier","GinibrePoincare.Analysis.GinibreFullSemigroupGenerator","GinibrePoincare.Analysis.GinibreFullSemigroupInfinitesimal","GinibrePoincare.Analysis.GinibreFullSemigroupL1","GinibrePoincare.Analysis.GinibreFullSemigroupMarkov","GinibrePoincare.Analysis.GinibreFullSemigroupMultiplier","GinibrePoincare.Analysis.GinibreFullSemigroupOrder","GinibrePoincare.Analysis.GinibreFullSemigroupOrderTest","GinibrePoincare.Analysis.GinibreFullSemigroupPaperSpeed","GinibrePoincare.Analysis.GinibreFullSemigroupRealInvariant","GinibrePoincare.Analysis.GinibreFullSemigroupRegularity","GinibrePoincare.Analysis.GinibreFullSemigroupRegularityDynamics","GinibrePoincare.Analysis.GinibreFullSemigroupWeakHeat","GinibrePoincare.Analysis.GinibreFullSemigroupWeakOrder","GinibrePoincare.Analysis.GinibreGeneratorDeficitAlgebra","GinibrePoincare.Analysis.GinibreGeneratorGradientCommutation","GinibrePoincare.Analysis.GinibreGeneratorL2","GinibrePoincare.Analysis.GinibreGradientPhaseNorm","GinibrePoincare.Analysis.GinibreGraphNormEquivalence","GinibrePoincare.Analysis.GinibreHamiltonian","GinibrePoincare.Analysis.GinibreHamiltonianActualStationaryOUReversal","GinibrePoincare.Analysis.GinibreHamiltonianBrownianRestart","GinibrePoincare.Analysis.GinibreHamiltonianCanonicalRestart","GinibrePoincare.Analysis.GinibreHamiltonianCenterFunctional","GinibrePoincare.Analysis.GinibreHamiltonianChapmanKolmogorov","GinibrePoincare.Analysis.GinibreHamiltonianCoercivity","GinibrePoincare.Analysis.GinibreHamiltonianCollision","GinibrePoincare.Analysis.GinibreHamiltonianCompactDrift","GinibrePoincare.Analysis.GinibreHamiltonianCompactPathWeight","GinibrePoincare.Analysis.GinibreHamiltonianCompletedProductBrownian","GinibrePoincare.Analysis.GinibreHamiltonianCompletedStationaryReference","GinibrePoincare.Analysis.GinibreHamiltonianConditionalMarkov","GinibrePoincare.Analysis.GinibreHamiltonianConfigurationOUReference","GinibrePoincare.Analysis.GinibreHamiltonianContinuation","GinibrePoincare.Analysis.GinibreHamiltonianContinuousClosedStopping","GinibrePoincare.Analysis.GinibreHamiltonianContinuousPathIndependence","GinibrePoincare.Analysis.GinibreHamiltonianCoreTestExpectation","GinibrePoincare.Analysis.GinibreHamiltonianDrift","GinibrePoincare.Analysis.GinibreHamiltonianEquilibriumProductLaw","GinibrePoincare.Analysis.GinibreHamiltonianFactorization","GinibrePoincare.Analysis.GinibreHamiltonianFirstLevel","GinibrePoincare.Analysis.GinibreHamiltonianGaussianCoordinateLaw","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUContinuousReversal","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUCovariance","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUFiniteLaw","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOULimit","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUProcess","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUProductReversal","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUReversal","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUReversalWeight","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOURiemann","GinibrePoincare.Analysis.GinibreHamiltonianGaussianOUWholeReversal","GinibrePoincare.Analysis.GinibreHamiltonianGenerator","GinibrePoincare.Analysis.GinibreHamiltonianGradientPathMeasure","GinibrePoincare.Analysis.GinibreHamiltonianGradientPathWeight","GinibrePoincare.Analysis.GinibreHamiltonianInitialCollisionNormalization","GinibrePoincare.Analysis.GinibreHamiltonianInitialDensityCancellation","GinibrePoincare.Analysis.GinibreHamiltonianInitialMeasureIdentification","GinibrePoincare.Analysis.GinibreHamiltonianInteractionEnergy","GinibrePoincare.Analysis.GinibreHamiltonianInteractionPotential","GinibrePoincare.Analysis.GinibreHamiltonianInteractionTilt","GinibrePoincare.Analysis.GinibreHamiltonianItoGenerator","GinibrePoincare.Analysis.GinibreHamiltonianJointEvaluation","GinibrePoincare.Analysis.GinibreHamiltonianJointEvaluationStability","GinibrePoincare.Analysis.GinibreHamiltonianJointLifetime","GinibrePoincare.Analysis.GinibreHamiltonianJointStability","GinibrePoincare.Analysis.GinibreHamiltonianJointTube","GinibrePoincare.Analysis.GinibreHamiltonianKernelGenerator","GinibrePoincare.Analysis.GinibreHamiltonianKilledExhaustionIntegration","GinibrePoincare.Analysis.GinibreHamiltonianKilledMixtureIntegration","GinibrePoincare.Analysis.GinibreHamiltonianKilledOUPathMeasure","GinibrePoincare.Analysis.GinibreHamiltonianLaplacian","GinibrePoincare.Analysis.GinibreHamiltonianLevelLocalization","GinibrePoincare.Analysis.GinibreHamiltonianLocalizationLimit","GinibrePoincare.Analysis.GinibreHamiltonianLocalizedIto","GinibrePoincare.Analysis.GinibreHamiltonianMarkovLaw","GinibrePoincare.Analysis.GinibreHamiltonianMaximalBlowup","GinibrePoincare.Analysis.GinibreHamiltonianMaximalCausality","GinibrePoincare.Analysis.GinibreHamiltonianMaximalEvaluation","GinibrePoincare.Analysis.GinibreHamiltonianMaximalEvaluationStability","GinibrePoincare.Analysis.GinibreHamiltonianMaximalGlobal","GinibrePoincare.Analysis.GinibreHamiltonianMaximalLevel","GinibrePoincare.Analysis.GinibreHamiltonianMaximalLifetime","GinibrePoincare.Analysis.GinibreHamiltonianMaximalNoiseStability","GinibrePoincare.Analysis.GinibreHamiltonianMaximalNoiseTopology","GinibrePoincare.Analysis.GinibreHamiltonianMaximalPast","GinibrePoincare.Analysis.GinibreHamiltonianMaximalPath","GinibrePoincare.Analysis.GinibreHamiltonianMaximalSegments","GinibrePoincare.Analysis.GinibreHamiltonianMaximalTimeContinuity","GinibrePoincare.Analysis.GinibreHamiltonianMetropolisBalance","GinibrePoincare.Analysis.GinibreHamiltonianMetropolisInvariant","GinibrePoincare.Analysis.GinibreHamiltonianOUActionExpansion","GinibrePoincare.Analysis.GinibreHamiltonianOUActionLocality","GinibrePoincare.Analysis.GinibreHamiltonianOUActionWeight","GinibrePoincare.Analysis.GinibreHamiltonianOUCompactClippedFlow","GinibrePoincare.Analysis.GinibreHamiltonianOUCompactLocalFlow","GinibrePoincare.Analysis.GinibreHamiltonianOUCompactStoppedSelection","GinibrePoincare.Analysis.GinibreHamiltonianOUCoordinateAssembly","GinibrePoincare.Analysis.GinibreHamiltonianOUInteractionDensity","GinibrePoincare.Analysis.GinibreHamiltonianOUInteractionIto","GinibrePoincare.Analysis.GinibreHamiltonianOUJointPath","GinibrePoincare.Analysis.GinibreHamiltonianOUReferenceInteractionDensity","GinibrePoincare.Analysis.GinibreHamiltonianOUReferenceInteractionIto","GinibrePoincare.Analysis.GinibreHamiltonianOUReferenceProcess","GinibrePoincare.Analysis.GinibreHamiltonianOUReferenceStopped","GinibrePoincare.Analysis.GinibreHamiltonianOUReferenceSublevelStopped","GinibrePoincare.Analysis.GinibreHamiltonianOUReversibility","GinibrePoincare.Analysis.GinibreHamiltonianOUSublevelInteractionDensity","GinibrePoincare.Analysis.GinibreHamiltonianOUSublevelInteractionIto","GinibrePoincare.Analysis.GinibreHamiltonianOriginalEquilibriumMarginals","GinibrePoincare.Analysis.GinibreHamiltonianOriginalEquilibriumReversal","GinibrePoincare.Analysis.GinibreHamiltonianOriginalKilledInitialIntegration","GinibrePoincare.Analysis.GinibreHamiltonianPairs","GinibrePoincare.Analysis.GinibreHamiltonianPathUniqueness","GinibrePoincare.Analysis.GinibreHamiltonianProcessFactorization","GinibrePoincare.Analysis.GinibreHamiltonianProductTransition","GinibrePoincare.Analysis.GinibreHamiltonianProjectedNoise","GinibrePoincare.Analysis.GinibreHamiltonianRadialGenerator","GinibrePoincare.Analysis.GinibreHamiltonianRadialIto","GinibrePoincare.Analysis.GinibreHamiltonianReversalMarginals","GinibrePoincare.Analysis.GinibreHamiltonianScalarOUPairFunction","GinibrePoincare.Analysis.GinibreHamiltonianStateTransitionKernel","GinibrePoincare.Analysis.GinibreHamiltonianStoppedTestExpectation","GinibrePoincare.Analysis.GinibreHamiltonianSublevelPathExhaustion","GinibrePoincare.Analysis.GinibreHamiltonianSublevels","GinibrePoincare.Analysis.GinibreHamiltonianTransitionKernel","GinibrePoincare.Analysis.GinibreHamiltonianTubeStability","GinibrePoincare.Analysis.GinibreIntegrationByParts","GinibrePoincare.Analysis.GinibreInteriorSobolevMollification","GinibrePoincare.Analysis.GinibreInteriorWeakGradient","GinibrePoincare.Analysis.GinibreLebesgueL2Transfer","GinibrePoincare.Analysis.GinibreLinearStatisticDifferential","GinibrePoincare.Analysis.GinibreLinearStatisticPoincare","GinibrePoincare.Analysis.GinibreLiteralProjectionGeometry","GinibrePoincare.Analysis.GinibreLocalSobolev","GinibrePoincare.Analysis.GinibreMassFiniteness","GinibrePoincare.Analysis.GinibreMassPositivity","GinibrePoincare.Analysis.GinibreMixedGreenIdentity","GinibrePoincare.Analysis.GinibreNonsymmetricCounterexample","GinibrePoincare.Analysis.GinibreNonsymmetricCounterexampleCoordinates","GinibrePoincare.Analysis.GinibreNonsymmetricCounterexampleMoments","GinibrePoincare.Analysis.GinibreOUComplexTransition","GinibrePoincare.Analysis.GinibreOUTransition","GinibrePoincare.Analysis.GinibreOUTransitionSemigroup","GinibrePoincare.Analysis.GinibreOneParticleSpectrum","GinibrePoincare.Analysis.GinibrePairRadius","GinibrePoincare.Analysis.GinibrePermutationAverage","GinibrePoincare.Analysis.GinibrePermutationGradient","GinibrePoincare.Analysis.GinibrePhaseCoordinates","GinibrePoincare.Analysis.GinibrePhaseRegularSobolev","GinibrePoincare.Analysis.GinibrePhaseSeparation","GinibrePoincare.Analysis.GinibrePointwiseBochner","GinibrePoincare.Analysis.GinibrePointwiseBochnerDirectional","GinibrePoincare.Analysis.GinibrePointwiseBochnerFormula","GinibrePoincare.Analysis.GinibrePointwiseBochnerOperator","GinibrePoincare.Analysis.GinibrePointwiseCurvature","GinibrePoincare.Analysis.GinibrePointwiseCurvatureTangent","GinibrePoincare.Analysis.GinibreRadialCompactWeakGradient","GinibrePoincare.Analysis.GinibreRadialGamma","GinibrePoincare.Analysis.GinibreRadialInteriorMollification","GinibrePoincare.Analysis.GinibreRadialLocalSobolev","GinibrePoincare.Analysis.GinibreRadialPhaseMollification","GinibrePoincare.Analysis.GinibreRadialPhaseWeakTests","GinibrePoincare.Analysis.GinibreRadialWeakDomainEquality","GinibrePoincare.Analysis.GinibreRadialWeakSobolevApproximation","GinibrePoincare.Analysis.GinibreRadiusNotHolomorphic","GinibrePoincare.Analysis.GinibreRealCoreClosureEquivalence","GinibrePoincare.Analysis.GinibreRelativePhaseInvariance","GinibrePoincare.Analysis.GinibreSmoothDistributionalGradient","GinibrePoincare.Analysis.GinibreSpatialCutoffs","GinibrePoincare.Analysis.GinibreStochasticAdaptedLocalSelection","GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedMoments","GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedOrthogonality","GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedSum","GinibrePoincare.Analysis.GinibreStochasticAugmentedMixedVariation","GinibrePoincare.Analysis.GinibreStochasticAugmentedPredictableQuadratic","GinibrePoincare.Analysis.GinibreStochasticAugmentedQuadraticOrthogonality","GinibrePoincare.Analysis.GinibreStochasticAugmentedQuadraticSum","GinibrePoincare.Analysis.GinibreStochasticAugmentedQuadraticVariation","GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedDiagonal","GinibrePoincare.Analysis.GinibreStochasticAugmentedWeightedHessian","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyBracket","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyCrossBracket","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyFiltration","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyGaussian","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyMartingale","GinibrePoincare.Analysis.GinibreStochasticBrownianFamilyPast","GinibrePoincare.Analysis.GinibreStochasticBrownianItoSquare","GinibrePoincare.Analysis.GinibreStochasticBrownianLinearOrthogonality","GinibrePoincare.Analysis.GinibreStochasticBrownianPlanarCrossConditional","GinibrePoincare.Analysis.GinibreStochasticBrownianPlanarIncrement","GinibrePoincare.Analysis.GinibreStochasticBrownianPlanarPredictableSquare","GinibrePoincare.Analysis.GinibreStochasticBrownianPredictableIsometry","GinibrePoincare.Analysis.GinibreStochasticBrownianPredictableLinear","GinibrePoincare.Analysis.GinibreStochasticBrownianQuadraticInnovation","GinibrePoincare.Analysis.GinibreStochasticBrownianQuadraticOrthogonality","GinibrePoincare.Analysis.GinibreStochasticBrownianQuadraticSums","GinibrePoincare.Analysis.GinibreStochasticBrownianQuadraticVariation","GinibrePoincare.Analysis.GinibreStochasticBrownianSums","GinibrePoincare.Analysis.GinibreStochasticBrownianWeightedQuadratic","GinibrePoincare.Analysis.GinibreStochasticBrownianWeightedQuadraticSum","GinibrePoincare.Analysis.GinibreStochasticBrownianWeightedQuadraticVariation","GinibrePoincare.Analysis.GinibreStochasticCIRCoefficientProcess","GinibrePoincare.Analysis.GinibreStochasticCIRConditionalMoment","GinibrePoincare.Analysis.GinibreStochasticCIRDrivenLocal","GinibrePoincare.Analysis.GinibreStochasticCIRExponentialMartingale","GinibrePoincare.Analysis.GinibreStochasticCIRFullNoiseSums","GinibrePoincare.Analysis.GinibreStochasticCIRGenerator","GinibrePoincare.Analysis.GinibreStochasticCIRIntegral","GinibrePoincare.Analysis.GinibreStochasticCIRItoSquare","GinibrePoincare.Analysis.GinibreStochasticCIRMoments","GinibrePoincare.Analysis.GinibreStochasticCIRNoiseCoefficient","GinibrePoincare.Analysis.GinibreStochasticCIRNoiseSums","GinibrePoincare.Analysis.GinibreStochasticCIRRealization","GinibrePoincare.Analysis.GinibreStochasticCIRTransition","GinibrePoincare.Analysis.GinibreStochasticCausalFlowAdaptation","GinibrePoincare.Analysis.GinibreStochasticCenterBarrierExpectation","GinibrePoincare.Analysis.GinibreStochasticCenterBarrierIto","GinibrePoincare.Analysis.GinibreStochasticCenterBeforeHitting","GinibrePoincare.Analysis.GinibreStochasticCenterBrownian","GinibrePoincare.Analysis.GinibreStochasticCenterCIRNoiseCoefficient","GinibrePoincare.Analysis.GinibreStochasticCenterCIRUnrestrictedRealization","GinibrePoincare.Analysis.GinibreStochasticCenterDirection","GinibrePoincare.Analysis.GinibreStochasticCenterGlobalNonvanishing","GinibrePoincare.Analysis.GinibreStochasticCenterHittingExhaustion","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiFunctional","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiGenerator","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiGlobal","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiIto","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiNoiseCoefficient","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiRegularization","GinibrePoincare.Analysis.GinibreStochasticCenterLampertiScalarFunctional","GinibrePoincare.Analysis.GinibreStochasticCenterLocalNonvanishing","GinibrePoincare.Analysis.GinibreStochasticCenterLogGenerator","GinibrePoincare.Analysis.GinibreStochasticCenterLogRegularization","GinibrePoincare.Analysis.GinibreStochasticCenterLogVanishing","GinibrePoincare.Analysis.GinibreStochasticCenterNoiseCoefficients","GinibrePoincare.Analysis.GinibreStochasticCenterRadialDriverIndependence","GinibrePoincare.Analysis.GinibreStochasticCenterSmallProbability","GinibrePoincare.Analysis.GinibreStochasticCenterSmallStopping","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredAmplitude","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredDrivenLocal","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredFullNoiseSums","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredIntegral","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredNoiseSums","GinibrePoincare.Analysis.GinibreStochasticCenterSquaredRealization","GinibrePoincare.Analysis.GinibreStochasticCenterZeroBrownian","GinibrePoincare.Analysis.GinibreStochasticCenterZeroCIRDrivenLocal","GinibrePoincare.Analysis.GinibreStochasticCenterZeroDirection","GinibrePoincare.Analysis.GinibreStochasticCenterZeroDriverIndependence","GinibrePoincare.Analysis.GinibreStochasticCenterZeroDriverRecovery","GinibrePoincare.Analysis.GinibreStochasticCenterZeroGaussian","GinibrePoincare.Analysis.GinibreStochasticCenterZeroIntegral","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementContinuous","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementGlobal","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementIto","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementLocal","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementLocalization","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiIncrementShift","GinibrePoincare.Analysis.GinibreStochasticCenterZeroLampertiRecovery","GinibrePoincare.Analysis.GinibreStochasticCenterZeroOULaw","GinibrePoincare.Analysis.GinibreStochasticCenterZeroPathEvent","GinibrePoincare.Analysis.GinibreStochasticCenterZeroPositiveTime","GinibrePoincare.Analysis.GinibreStochasticCenterZeroRestartNonvanishing","GinibrePoincare.Analysis.GinibreStochasticCenterZeroSpeed","GinibrePoincare.Analysis.GinibreStochasticCompactDerivativeMeasurability","GinibrePoincare.Analysis.GinibreStochasticCompactGradientIntegral","GinibrePoincare.Analysis.GinibreStochasticCompactHessianCorrection","GinibrePoincare.Analysis.GinibreStochasticCompactItoIntegral","GinibrePoincare.Analysis.GinibreStochasticCompactItoMartingale","GinibrePoincare.Analysis.GinibreStochasticCompactStoppedSelection","GinibrePoincare.Analysis.GinibreStochasticCompactTaylorMeasurability","GinibrePoincare.Analysis.GinibreStochasticCompactTestCoefficients","GinibrePoincare.Analysis.GinibreStochasticCompactTestDynkin","GinibrePoincare.Analysis.GinibreStochasticCompactTestLaplace","GinibrePoincare.Analysis.GinibreStochasticConditionalKernel","GinibrePoincare.Analysis.GinibreStochasticConfigurationBrownianBracket","GinibrePoincare.Analysis.GinibreStochasticConfigurationBrownianCoordinates","GinibrePoincare.Analysis.GinibreStochasticConfigurationBrownianIncrement","GinibrePoincare.Analysis.GinibreStochasticConfigurationBrownianMartingale","GinibrePoincare.Analysis.GinibreStochasticConfigurationHessianSum","GinibrePoincare.Analysis.GinibreStochasticContinuousConfigurationNoise","GinibrePoincare.Analysis.GinibreStochasticContinuousFieldIntegral","GinibrePoincare.Analysis.GinibreStochasticContinuousGradientIntegral","GinibrePoincare.Analysis.GinibreStochasticContinuousLocalIdentity","GinibrePoincare.Analysis.GinibreStochasticContinuousNoisePath","GinibrePoincare.Analysis.GinibreStochasticContinuousPastPath","GinibrePoincare.Analysis.GinibreStochasticContinuousStoppingTime","GinibrePoincare.Analysis.GinibreStochasticFamilyQuadraticSum","GinibrePoincare.Analysis.GinibreStochasticFullTwoRadiusRealization","GinibrePoincare.Analysis.GinibreStochasticGaussianFourthMoment","GinibrePoincare.Analysis.GinibreStochasticGaussianLimit","GinibrePoincare.Analysis.GinibreStochasticGaussianPiCrossMoments","GinibrePoincare.Analysis.GinibreStochasticGaussianSquareMoments","GinibrePoincare.Analysis.GinibreStochasticGeneratorCompensator","GinibrePoincare.Analysis.GinibreStochasticGeneratorNormalization","GinibrePoincare.Analysis.GinibreStochasticGlobalTestIto","GinibrePoincare.Analysis.GinibreStochasticGlobalUniqueness","GinibrePoincare.Analysis.GinibreStochasticGradientIntegralAllHorizons","GinibrePoincare.Analysis.GinibreStochasticHamiltonianIto","GinibrePoincare.Analysis.GinibreStochasticHamiltonianItoTerminal","GinibrePoincare.Analysis.GinibreStochasticIndependentBlocks","GinibrePoincare.Analysis.GinibreStochasticIntegralUntilIdentity","GinibrePoincare.Analysis.GinibreStochasticItoUntilStopping","GinibrePoincare.Analysis.GinibreStochasticLampertiFunctional","GinibrePoincare.Analysis.GinibreStochasticLampertiGenerator","GinibrePoincare.Analysis.GinibreStochasticLampertiGlobal","GinibrePoincare.Analysis.GinibreStochasticLampertiIto","GinibrePoincare.Analysis.GinibreStochasticLampertiNoiseSums","GinibrePoincare.Analysis.GinibreStochasticLocalExistence","GinibrePoincare.Analysis.GinibreStochasticLocalTestIto","GinibrePoincare.Analysis.GinibreStochasticLocalTestItoIntegral","GinibrePoincare.Analysis.GinibreStochasticLocalizationExhaustion","GinibrePoincare.Analysis.GinibreStochasticMeanSquareInProbability","GinibrePoincare.Analysis.GinibreStochasticMeasurableLocalSelection","GinibrePoincare.Analysis.GinibreStochasticNoncollision","GinibrePoincare.Analysis.GinibreStochasticOUConvolution","GinibrePoincare.Analysis.GinibreStochasticOUFunctional","GinibrePoincare.Analysis.GinibreStochasticOUGaussian","GinibrePoincare.Analysis.GinibreStochasticOUIndependent","GinibrePoincare.Analysis.GinibreStochasticOUInnovation","GinibrePoincare.Analysis.GinibreStochasticOUItoSquare","GinibrePoincare.Analysis.GinibreStochasticOUJointLaw","GinibrePoincare.Analysis.GinibreStochasticOUPast","GinibrePoincare.Analysis.GinibreStochasticOUPath","GinibrePoincare.Analysis.GinibreStochasticOUPlanarInnovation","GinibrePoincare.Analysis.GinibreStochasticOUPlanarMarkov","GinibrePoincare.Analysis.GinibreStochasticOUQuadraticConditional","GinibrePoincare.Analysis.GinibreStochasticOURiemann","GinibrePoincare.Analysis.GinibreStochasticOUStep","GinibrePoincare.Analysis.GinibreStochasticOUTimeChange","GinibrePoincare.Analysis.GinibreStochasticOUWeight","GinibrePoincare.Analysis.GinibreStochasticOUWholePastMarkov","GinibrePoincare.Analysis.GinibreStochasticOneParticle","GinibrePoincare.Analysis.GinibreStochasticOneParticleLaw","GinibrePoincare.Analysis.GinibreStochasticOneParticleMarkov","GinibrePoincare.Analysis.GinibreStochasticOneParticleProjection","GinibrePoincare.Analysis.GinibreStochasticOneParticleRadius","GinibrePoincare.Analysis.GinibreStochasticOrthogonalSquareSum","GinibrePoincare.Analysis.GinibreStochasticPastAugmentation","GinibrePoincare.Analysis.GinibreStochasticPlanarGaussianRotation","GinibrePoincare.Analysis.GinibreStochasticPredictableInnovation","GinibrePoincare.Analysis.GinibreStochasticProbabilityOperations","GinibrePoincare.Analysis.GinibreStochasticProbabilityRestriction","GinibrePoincare.Analysis.GinibreStochasticPuncturedUnitFieldBrownian","GinibrePoincare.Analysis.GinibreStochasticPuncturedUnitFieldGlobalIntegral","GinibrePoincare.Analysis.GinibreStochasticPuncturedUnitFieldIntegral","GinibrePoincare.Analysis.GinibreStochasticPuncturedUnitFieldPartialMeanSquare","GinibrePoincare.Analysis.GinibreStochasticRadialBrownian","GinibrePoincare.Analysis.GinibreStochasticRadialCenterIndependence","GinibrePoincare.Analysis.GinibreStochasticRadialDirection","GinibrePoincare.Analysis.GinibreStochasticRadialGlobalIntegral","GinibrePoincare.Analysis.GinibreStochasticRadialGradient","GinibrePoincare.Analysis.GinibreStochasticRadialIntegral","GinibrePoincare.Analysis.GinibreStochasticRadialPath","GinibrePoincare.Analysis.GinibreStochasticRadiusRotation","GinibrePoincare.Analysis.GinibreStochasticRestrictedDriftRiemann","GinibrePoincare.Analysis.GinibreStochasticRestrictedHessianCorrection","GinibrePoincare.Analysis.GinibreStochasticRestrictedIto","GinibrePoincare.Analysis.GinibreStochasticRestrictedTaylorRemainder","GinibrePoincare.Analysis.GinibreStochasticSquareRootRadius","GinibrePoincare.Analysis.GinibreStochasticStationaryTwoRadiusLaw","GinibrePoincare.Analysis.GinibreStochasticStoppedLocalSelection","GinibrePoincare.Analysis.GinibreStochasticTestCompensator","GinibrePoincare.Analysis.GinibreStochasticTransitionBoundedOperator","GinibrePoincare.Analysis.GinibreStochasticTransitionBoundedResolvent","GinibrePoincare.Analysis.GinibreStochasticTransitionCompactResolvent","GinibrePoincare.Analysis.GinibreStochasticTransitionContinuousMean","GinibrePoincare.Analysis.GinibreStochasticTransitionCoreDuhamel","GinibrePoincare.Analysis.GinibreStochasticTransitionCoreResolvent","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Continuity","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Operator","GinibrePoincare.Analysis.GinibreStochasticTransitionL2ProductPairing","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Pullback","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Resolvent","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Sampling","GinibrePoincare.Analysis.GinibreStochasticTransitionL2Semigroup","GinibrePoincare.Analysis.GinibreStochasticTransitionL2ZeroSpeed","GinibrePoincare.Analysis.GinibreStochasticTransitionLaplaceCore","GinibrePoincare.Analysis.GinibreStochasticTransitionLaplaceFubini","GinibrePoincare.Analysis.GinibreStochasticTransitionMarkovMean","GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationDynamics","GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationMaximal","GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationMean","GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationNoise","GinibrePoincare.Analysis.GinibreStochasticTransitionPermutationOperator","GinibrePoincare.Analysis.GinibreStochasticTransitionResolventIdentification","GinibrePoincare.Analysis.GinibreStochasticTransitionResolventOperator","GinibrePoincare.Analysis.GinibreStochasticTransitionSemigroupIdentification","GinibrePoincare.Analysis.GinibreStochasticTransitionSymmetricOperator","GinibrePoincare.Analysis.GinibreStochasticTransitionWeightedLaplace","GinibrePoincare.Analysis.GinibreStochasticTwoRadiusRealization","GinibrePoincare.Analysis.GinibreStochasticUnitFieldBrownian","GinibrePoincare.Analysis.GinibreStochasticUnitFieldGlobalIntegral","GinibrePoincare.Analysis.GinibreStochasticUnitFieldIntegral","GinibrePoincare.Analysis.GinibreStochasticUnitFieldPartialMeanSquare","GinibrePoincare.Analysis.GinibreStochasticVolterraTaylorRemainder","GinibrePoincare.Analysis.GinibreStochasticWeightedSumMemLp","GinibrePoincare.Analysis.GinibreSymmetricWeakPoincare","GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedAdjointIdentification","GinibrePoincare.Analysis.GinibreTransitionAnalyticBoundedDense","GinibrePoincare.Analysis.GinibreTransitionAnalyticCaccioppoli","GinibrePoincare.Analysis.GinibreTransitionAnalyticCore","GinibrePoincare.Analysis.GinibreTransitionAnalyticCutoffExhaustion","GinibrePoincare.Analysis.GinibreTransitionAnalyticDissipativeUniqueness","GinibrePoincare.Analysis.GinibreTransitionAnalyticEnergyCompactness","GinibrePoincare.Analysis.GinibreTransitionAnalyticGlobalEnergy","GinibrePoincare.Analysis.GinibreTransitionAnalyticGraphUniqueness","GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceBounds","GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOperator","GinibrePoincare.Analysis.GinibreTransitionAnalyticLaplaceOrbit","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularity","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityAdjointDensity","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityBessel","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactData","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactExhaustion","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCompactTests","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConfigurationCutoff","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityConvolution","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinateBasis","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinateEquation","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinateLp","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinateWeak","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityCoordinates","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityCutoff","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityDivergence","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityEquation","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityDensityQuotient","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityGluing","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityInterior","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityInteriorCutoff","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalization","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityLocalizedData","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityMollifiedEquation","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityProduct","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealDerivative","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealIndicator","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRealTests","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityRestrictedData","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityTemperedEquation","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityTestIntegrability","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityWeakDerivatives","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityWeakProduct","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityWeakUniqueness","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalRegularityWeightedData","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingApproximation","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingContinuity","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingDistributional","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingGlobalEnergy","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingGreen","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingIdentity","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingLeibniz","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingLocalIntegrability","GinibrePoincare.Analysis.GinibreTransitionAnalyticLocalWeakTestingLocalization","GinibrePoincare.Analysis.GinibreTransitionAnalyticPathLaw","GinibrePoincare.Analysis.GinibreTransitionAnalyticRealGraphOrbit","GinibrePoincare.Analysis.GinibreTransitionAnalyticResolventSemigroupComparison","GinibrePoincare.Analysis.GinibreTransitionAnalyticUnrestrictedWeakComparison","GinibrePoincare.Analysis.GinibreTransitionAnalyticWeakCore","GinibrePoincare.Analysis.GinibreTransitionAnalyticWeakSymmetry","GinibrePoincare.Analysis.GinibreTransitionAnalyticZeroSpeed","GinibrePoincare.Analysis.GinibreTwoRadiusEquilibriumLaw","GinibrePoincare.Analysis.GinibreValueTruncationChainLimits","GinibrePoincare.Analysis.GinibreValueTruncationL2","GinibrePoincare.Analysis.GinibreValueTruncationWeakChain","GinibrePoincare.Analysis.GinibreWeakGradient","GinibrePoincare.Analysis.GinibreWeakGradientPhase","GinibrePoincare.Analysis.GinibreWeakGradientSupport","GinibrePoincare.Analysis.GinibreWeakPermutation","GinibrePoincare.Analysis.GinibreWeakSobolevMultipliers","GinibrePoincare.Analysis.GinibreWeakSobolevTruncation","GinibrePoincare.Analysis.GinibreWeightedInteriorMollification","GinibrePoincare.Analysis.GinibreWeightedRadialInteriorMollification","GinibrePoincare.Analysis.GinibreZeroPairAvoidance","GinibrePoincare.Analysis.GinibreZeroPairCutoff","GinibrePoincare.Analysis.GinibreZeroPairCutoffEnergy","GinibrePoincare.Analysis.GinibreZeroPairIntegrability","GinibrePoincare.Analysis.GinibreZeroPairL2Approximation","GinibrePoincare.Analysis.GlobalPhaseAction","GinibrePoincare.Analysis.GroundStateDbar","GinibrePoincare.Analysis.HermiteBinomialIdentity","GinibrePoincare.Analysis.HermiteEnergy","GinibrePoincare.Analysis.HermiteInverseSquareRoot","GinibrePoincare.Analysis.HermiteL2Family","GinibrePoincare.Analysis.HermiteLaguerreOperator","GinibrePoincare.Analysis.HermiteMonomialSpan","GinibrePoincare.Analysis.HermiteOrnsteinUhlenbeck","GinibrePoincare.Analysis.HermiteOrthogonalityCombinatorics","GinibrePoincare.Analysis.HermiteParsevalModes","GinibrePoincare.Analysis.HermiteRodrigues","GinibrePoincare.Analysis.HermiteRodriguesGaussian","GinibrePoincare.Analysis.HermiteRodriguesHolomorphicLowering","GinibrePoincare.Analysis.HermiteRodriguesIteration","GinibrePoincare.Analysis.HermiteRodriguesMultivariate","GinibrePoincare.Analysis.HermiteRodriguesNormalization","GinibrePoincare.Analysis.HermiteRodriguesPolynomial","GinibrePoincare.Analysis.HermiteRodriguesRaising","GinibrePoincare.Analysis.HermiteRodriguesSmooth","GinibrePoincare.Analysis.HermiteRodriguesTensor","GinibrePoincare.Analysis.HermiteSecondDbarCombinatorics","GinibrePoincare.Analysis.HermiteSecondDbarEnergy","GinibrePoincare.Analysis.HermiteSecondDbarInfiniteEnergy","GinibrePoincare.Analysis.HermiteSecondDbarWeakClosure","GinibrePoincare.Analysis.HermiteWeightedEnergy","GinibrePoincare.Analysis.HermiteWirtinger","GinibrePoincare.Analysis.HolomorphicQuotientPhaseFinite","GinibrePoincare.Analysis.HolomorphicQuotientPhaseProjection","GinibrePoincare.Analysis.HolomorphicVandermondeDivision","GinibrePoincare.Analysis.HolomorphicVandermondeL2Closure","GinibrePoincare.Analysis.HomogeneousRadialMeasure","GinibrePoincare.Analysis.IndependentNoiseMixture","GinibrePoincare.Analysis.IntegralEntropyTensorization","GinibrePoincare.Analysis.KostlanDiagonalIdentity","GinibrePoincare.Analysis.KostlanEntropyTransfer","GinibrePoincare.Analysis.KostlanGammaLaw","GinibrePoincare.Analysis.KostlanProductLaw","GinibrePoincare.Analysis.KostlanRadialTransfer","GinibrePoincare.Analysis.L2BoundedCoefficientConvergence","GinibrePoincare.Analysis.L2RepresentativeBridges","GinibrePoincare.Analysis.LaguerreGammaNondegeneracy","GinibrePoincare.Analysis.LaguerreGammaOrthogonality","GinibrePoincare.Analysis.LebesgueL2Convolution","GinibrePoincare.Analysis.LebesgueL2Mollification","GinibrePoincare.Analysis.LebesgueL2MollificationMaps","GinibrePoincare.Analysis.LipschitzMollification","GinibrePoincare.Analysis.LogSobolevInequality","GinibrePoincare.Analysis.MagnitudeGradient","GinibrePoincare.Analysis.MagnitudeNullSets","GinibrePoincare.Analysis.MatrixCayleyChart","GinibrePoincare.Analysis.MatrixDeterminantDerivative","GinibrePoincare.Analysis.MatrixEigenvalueDerivative","GinibrePoincare.Analysis.MatrixEigenvalueProjector","GinibrePoincare.Analysis.MatrixGaussianH1Closure","GinibrePoincare.Analysis.MatrixGaussianH1LSI","GinibrePoincare.Analysis.MatrixGaussianLSI","GinibrePoincare.Analysis.MatrixGaussianMeasure","GinibrePoincare.Analysis.MatrixGaussianPoincare","GinibrePoincare.Analysis.MatrixGaussianUnitaryInvariant","GinibrePoincare.Analysis.MatrixGinibreSpectralLaw","GinibrePoincare.Analysis.MatrixGinibreSymmetrizedLaw","GinibrePoincare.Analysis.MatrixLabelPermutation","GinibrePoincare.Analysis.MatrixLiftEnergy","GinibrePoincare.Analysis.MatrixLocalEigenvalue","GinibrePoincare.Analysis.MatrixLocalSpectrum","GinibrePoincare.Analysis.MatrixOverlap","GinibrePoincare.Analysis.MatrixOverlapGradientIntegrability","GinibrePoincare.Analysis.MatrixOverlapLowerBound","GinibrePoincare.Analysis.MatrixPolynomialNull","GinibrePoincare.Analysis.MatrixRealDifferential","GinibrePoincare.Analysis.MatrixSchurAngularChart","GinibrePoincare.Analysis.MatrixSchurAngularDensity","GinibrePoincare.Analysis.MatrixSchurAtlasCover","GinibrePoincare.Analysis.MatrixSchurAtlasIntegration","GinibrePoincare.Analysis.MatrixSchurAtlasOverlap","GinibrePoincare.Analysis.MatrixSchurAtlasPartition","GinibrePoincare.Analysis.MatrixSchurChamberIntegration","GinibrePoincare.Analysis.MatrixSchurChambers","GinibrePoincare.Analysis.MatrixSchurChartDerivative","GinibrePoincare.Analysis.MatrixSchurCoordinates","GinibrePoincare.Analysis.MatrixSchurDecomposition","GinibrePoincare.Analysis.MatrixSchurDensity","GinibrePoincare.Analysis.MatrixSchurDiagonal","GinibrePoincare.Analysis.MatrixSchurDiagonalIntegration","GinibrePoincare.Analysis.MatrixSchurEntryVolume","GinibrePoincare.Analysis.MatrixSchurExponentialJacobian","GinibrePoincare.Analysis.MatrixSchurFrameDerivative","GinibrePoincare.Analysis.MatrixSchurFrameJacobian","GinibrePoincare.Analysis.MatrixSchurFullJacobian","GinibrePoincare.Analysis.MatrixSchurGaussianGlobal","GinibrePoincare.Analysis.MatrixSchurGaussianIntegration","GinibrePoincare.Analysis.MatrixSchurGlobalIntegration","GinibrePoincare.Analysis.MatrixSchurInjectiveIntegration","GinibrePoincare.Analysis.MatrixSchurJacobian","GinibrePoincare.Analysis.MatrixSchurLinearCoordinates","GinibrePoincare.Analysis.MatrixSchurLocalChart","GinibrePoincare.Analysis.MatrixSchurLocalIntegration","GinibrePoincare.Analysis.MatrixSchurMovingJacobian","GinibrePoincare.Analysis.MatrixSchurOrderedSlice","GinibrePoincare.Analysis.MatrixSchurOrderedSpectralLaw","GinibrePoincare.Analysis.MatrixSchurProductIntegration","GinibrePoincare.Analysis.MatrixSchurRealJacobian","GinibrePoincare.Analysis.MatrixSchurSortedDecomposition","GinibrePoincare.Analysis.MatrixSchurSortedDomain","GinibrePoincare.Analysis.MatrixSchurSpectralObservable","GinibrePoincare.Analysis.MatrixSchurSymmetricObservable","GinibrePoincare.Analysis.MatrixSchurUniformSlice","GinibrePoincare.Analysis.MatrixSchurUniqueness","GinibrePoincare.Analysis.MatrixSchurUpperGaussian","GinibrePoincare.Analysis.MatrixSchurUpperSplit","GinibrePoincare.Analysis.MatrixSimpleSpectrum","GinibrePoincare.Analysis.MatrixSkewCoordinates","GinibrePoincare.Analysis.MatrixSpatialCutoff","GinibrePoincare.Analysis.MatrixSpectralBasis","GinibrePoincare.Analysis.MatrixSpectralIntegralTransport","GinibrePoincare.Analysis.MatrixSpectralLaw","GinibrePoincare.Analysis.MatrixSpectralLawOne","GinibrePoincare.Analysis.MatrixSpectralLiftDifferential","GinibrePoincare.Analysis.MatrixSpectralLiftEntryAE","GinibrePoincare.Analysis.MatrixSpectralLiftEntryLp","GinibrePoincare.Analysis.MatrixSpectralLiftFullEntry","GinibrePoincare.Analysis.MatrixSpectralLiftGradientLp","GinibrePoincare.Analysis.MatrixSpectralLiftLSIFinite","GinibrePoincare.Analysis.MatrixSpectralLiftLSITransport","GinibrePoincare.Analysis.MatrixSpectralLiftLSIWeak","GinibrePoincare.Analysis.MatrixSpectralLiftPoincareFinite","GinibrePoincare.Analysis.MatrixSpectralProjector","GinibrePoincare.Analysis.MatrixSpectralSobolevCandidateLines","GinibrePoincare.Analysis.MatrixSpectralSobolevCompactMollification","GinibrePoincare.Analysis.MatrixSpectralSobolevCompactWeightedDomain","GinibrePoincare.Analysis.MatrixSpectralSobolevContinuity","GinibrePoincare.Analysis.MatrixSpectralSobolevCoordinates","GinibrePoincare.Analysis.MatrixSpectralSobolevCoreTransport","GinibrePoincare.Analysis.MatrixSpectralSobolevDensity","GinibrePoincare.Analysis.MatrixSpectralSobolevDensityTransport","GinibrePoincare.Analysis.MatrixSpectralSobolevDirections","GinibrePoincare.Analysis.MatrixSpectralSobolevFTC","GinibrePoincare.Analysis.MatrixSpectralSobolevFubini","GinibrePoincare.Analysis.MatrixSpectralSobolevFullWeightedDomain","GinibrePoincare.Analysis.MatrixSpectralSobolevImagSplit","GinibrePoincare.Analysis.MatrixSpectralSobolevLift","GinibrePoincare.Analysis.MatrixSpectralSobolevLineRemovability","GinibrePoincare.Analysis.MatrixSpectralSobolevLocalIntegrability","GinibrePoincare.Analysis.MatrixSpectralSobolevLocalSlices","GinibrePoincare.Analysis.MatrixSpectralSobolevMatrixLines","GinibrePoincare.Analysis.MatrixSpectralSobolevMultiplierL2","GinibrePoincare.Analysis.MatrixSpectralSobolevPolynomialDomain","GinibrePoincare.Analysis.MatrixSpectralSobolevPolynomialImagTests","GinibrePoincare.Analysis.MatrixSpectralSobolevPolynomialImagWeak","GinibrePoincare.Analysis.MatrixSpectralSobolevPolynomialTests","GinibrePoincare.Analysis.MatrixSpectralSobolevPolynomialWeak","GinibrePoincare.Analysis.MatrixSpectralSobolevProductGaussian","GinibrePoincare.Analysis.MatrixSpectralSobolevRealSplit","GinibrePoincare.Analysis.MatrixSpectralSobolevReindex","GinibrePoincare.Analysis.MatrixSpectralSobolevRoots","GinibrePoincare.Analysis.MatrixSpectralSobolevSlices","GinibrePoincare.Analysis.MatrixSpectralSobolevSpatialPairs","GinibrePoincare.Analysis.MatrixSpectralSobolevSpatialTruncation","GinibrePoincare.Analysis.MatrixSpectralSobolevSpectralWeak","GinibrePoincare.Analysis.MatrixSpectralSobolevWeakDomain","GinibrePoincare.Analysis.MatrixSpectralSobolevWeakMultiplier","GinibrePoincare.Analysis.MatrixSpectralSobolevWeightedCompact","GinibrePoincare.Analysis.MatrixSymmetricLift","GinibrePoincare.Analysis.MatrixSymmetrizedSpectralLaw","GinibrePoincare.Analysis.MatrixUnitaryCenteredPhaseFactorization","GinibrePoincare.Analysis.MatrixUnitaryDerivative","GinibrePoincare.Analysis.MatrixUnitaryDiagonalPhase","GinibrePoincare.Analysis.MatrixUnitaryFlagAtlas","GinibrePoincare.Analysis.MatrixUnitaryFlagSaturation","GinibrePoincare.Analysis.MatrixUnitaryFlagSlice","GinibrePoincare.Analysis.MatrixUnitaryLowerChart","GinibrePoincare.Analysis.MatrixUnitaryPhaseChart","GinibrePoincare.Analysis.MatrixUnitarySmallPhaseFactorization","GinibrePoincare.Analysis.MatrixUnitaryVolume","GinibrePoincare.Analysis.MatrixVolumeSimpleSpectrum","GinibrePoincare.Analysis.MeasureTransport","GinibrePoincare.Analysis.MultivariateComplexHermite","GinibrePoincare.Analysis.MultivariateHermiteIntegrability","GinibrePoincare.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